Boundary Value Problems, ISSN 1687-2762, 12/2016, Volume 2016, Issue 1, pp. 1 - 24

In this paper, we present the abstract results for the existence and uniqueness of the solution of nonlinear elliptic systems, parabolic systems and...

integro-differential systems | Mathematics | maximal monotone operator | parabolic systems | ( p , q ) $(p,q)$ -Laplacian | Ordinary Differential Equations | elliptic systems | Analysis | Difference and Functional Equations | Approximations and Expansions | 47H09 | coercive | Mathematics, general | 47H05 | Partial Differential Equations | (p,q)-Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | (p, q)-Laplacian | Theorems (Mathematics) | Boundary value problems | Usage | Differential equations | Tests, problems and exercises | Operators | Construction | Mathematical analysis | Uniqueness | Texts | Nonlinearity | Complement

integro-differential systems | Mathematics | maximal monotone operator | parabolic systems | ( p , q ) $(p,q)$ -Laplacian | Ordinary Differential Equations | elliptic systems | Analysis | Difference and Functional Equations | Approximations and Expansions | 47H09 | coercive | Mathematics, general | 47H05 | Partial Differential Equations | (p,q)-Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | (p, q)-Laplacian | Theorems (Mathematics) | Boundary value problems | Usage | Differential equations | Tests, problems and exercises | Operators | Construction | Mathematical analysis | Uniqueness | Texts | Nonlinearity | Complement

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 11

A new fixed point theorem for systems of nonlinear operator equations is established by means of topological degree theory and positively 1-homogeneous...

Mathematics, general | 47H10 | Mathematics | Fixed point theorem | positively 1-homogeneous operators | ( $$p_1, p_2$$ p 1 , p 2 )-Laplacian system | p | Laplacian system

Mathematics, general | 47H10 | Mathematics | Fixed point theorem | positively 1-homogeneous operators | ( $$p_1, p_2$$ p 1 , p 2 )-Laplacian system | p | Laplacian system

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 08/2016, Volume 141, pp. 139 - 166

We prove the continuity of the gradient of weak solutions to nonhomogeneous p(⋅)-Laplace systems with coefficients. We assume that the nonhomogeneous term...

Dini continuity | Gradient continuity | [formula omitted]-Laplacian | Lorentz space | p(·)-Laplacian | MATHEMATICS, APPLIED | INTEGRABILITY | MINIMA | DEGENERATE ELLIPTIC-SYSTEMS | EQUATIONS | POTENTIALS | MATHEMATICS | p(center dot)-Laplacian | VARIABLE EXPONENT | REGULARITY | GROWTH | FUNCTIONALS

Dini continuity | Gradient continuity | [formula omitted]-Laplacian | Lorentz space | p(·)-Laplacian | MATHEMATICS, APPLIED | INTEGRABILITY | MINIMA | DEGENERATE ELLIPTIC-SYSTEMS | EQUATIONS | POTENTIALS | MATHEMATICS | p(center dot)-Laplacian | VARIABLE EXPONENT | REGULARITY | GROWTH | FUNCTIONALS

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2014, Volume 59, Issue 7, pp. 1765 - 1777

The paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape. A new...

Laplace equations | Shape control | Shape | Stability | distributed control | Eigenvalues and eigenfunctions | Vectors | Stability analysis | Nickel | formation | graph Laplacian | Multi-agent systems | multi-agent systems | STABILIZATION | PERSISTENCE | STRATEGIES | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | AUTONOMOUS FORMATIONS | RIGIDITY | Distributed control | stability | AUTOMATION & CONTROL SYSTEMS | COOPERATIVE CONTROL | Control systems | Agents (artificial intelligence) | Law | Specifications | Eigenvalues | Formations | Expert systems | Linear control | Concentrates

Laplace equations | Shape control | Shape | Stability | distributed control | Eigenvalues and eigenfunctions | Vectors | Stability analysis | Nickel | formation | graph Laplacian | Multi-agent systems | multi-agent systems | STABILIZATION | PERSISTENCE | STRATEGIES | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | AUTONOMOUS FORMATIONS | RIGIDITY | Distributed control | stability | AUTOMATION & CONTROL SYSTEMS | COOPERATIVE CONTROL | Control systems | Agents (artificial intelligence) | Law | Specifications | Eigenvalues | Formations | Expert systems | Linear control | Concentrates

Journal Article

Proceedings of the IEEE, ISSN 0018-9219, 01/2007, Volume 95, Issue 1, pp. 215 - 233

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed...

Algorithm design and analysis | Multiagent systems | multi-agent systems | information fusion | Sensor fusion | synchronization of coupled oscillators | Information analysis | Convergence | graph Laplacians | cooperative control | Network topology | Failure analysis | Consensus algorithms | flocking | networked control systems | Robustness | Matrices | Performance analysis | Graph Laplacians | Flocking | Networked control systems | Cooperative control | Information fusion | Synchronization of coupled oscillators | Multi-agent systems | PROTOCOLS | COORDINATION | AGREEMENT | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | MOBILE ROBOTS | consensus algorithms | CONVERGENCE | AGENTS | Studies | Control theory | Networks | Algorithms | Information flow | Dynamics | Synchronism | Sensors | Dynamical systems | Joints

Algorithm design and analysis | Multiagent systems | multi-agent systems | information fusion | Sensor fusion | synchronization of coupled oscillators | Information analysis | Convergence | graph Laplacians | cooperative control | Network topology | Failure analysis | Consensus algorithms | flocking | networked control systems | Robustness | Matrices | Performance analysis | Graph Laplacians | Flocking | Networked control systems | Cooperative control | Information fusion | Synchronization of coupled oscillators | Multi-agent systems | PROTOCOLS | COORDINATION | AGREEMENT | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | MOBILE ROBOTS | consensus algorithms | CONVERGENCE | AGENTS | Studies | Control theory | Networks | Algorithms | Information flow | Dynamics | Synchronism | Sensors | Dynamical systems | Joints

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 06/2013, Volume 58, Issue 6, pp. 1511 - 1523

This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics,...

Protocols | Laplace equations | Additives | Robustness | Eigenvalues and eigenfunctions | Laplacian matrix | Synchronization | Equations | NETWORKS | AGENTS | ALGORITHMS | CONSENSUS PROBLEMS | OSCILLATORS | STABILITY | CONSENSUS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Analysis | Transfer functions | Feedback control systems | Innovations | Laplace transformation | Riccati equation | Multi-agent systems

Protocols | Laplace equations | Additives | Robustness | Eigenvalues and eigenfunctions | Laplacian matrix | Synchronization | Equations | NETWORKS | AGENTS | ALGORITHMS | CONSENSUS PROBLEMS | OSCILLATORS | STABILITY | CONSENSUS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Analysis | Transfer functions | Feedback control systems | Innovations | Laplace transformation | Riccati equation | Multi-agent systems

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 9

We establish Lyapunov-type inequalities for a system involving one-dimensional -Laplacian operators (). Next, the obtained inequalities are used to derive some...

generalized eigenvalues | (p, q) -Laplacian | system | generalized spectrum | Lyapunov-type inequalities | MATHEMATICS | MATHEMATICS, APPLIED | (p,q)-Laplacian | QUASI-LINEAR SYSTEMS | Operators | Inequalities | ( p , q ) $(p,q)$ -Laplacian

generalized eigenvalues | (p, q) -Laplacian | system | generalized spectrum | Lyapunov-type inequalities | MATHEMATICS | MATHEMATICS, APPLIED | (p,q)-Laplacian | QUASI-LINEAR SYSTEMS | Operators | Inequalities | ( p , q ) $(p,q)$ -Laplacian

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 14

In this paper, by using the least action principle, an existence result of nontrivial weak solutions for a class of fractional impulsive coupled systems with...

Mathematics | Fractional coupled systems | Clark’s theorem | The least action principle | ( p , q ) $(p,q)$ -Laplacian | Impulsive effects | Ordinary Differential Equations | Functional Analysis | Analysis | Multiplicity | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | (p, q)-Laplacian | BOUNDARY-VALUE-PROBLEMS | Clark's theorem | Growth disorders

Mathematics | Fractional coupled systems | Clark’s theorem | The least action principle | ( p , q ) $(p,q)$ -Laplacian | Impulsive effects | Ordinary Differential Equations | Functional Analysis | Analysis | Multiplicity | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | (p, q)-Laplacian | BOUNDARY-VALUE-PROBLEMS | Clark's theorem | Growth disorders

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2019, Volume 2019, Issue 1, pp. 1 - 11

In this paper, we prove that the following (p1,p2,…,pn) $(p_{1},p_{2},\ldots,p_{n})$-Laplacian elliptic system with a nonsmooth potential has at least three...

Multiple solutions | Ordinary Differential Equations | Nonsmooth critical point | Variational methods | Locally Lipschitz | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | ( p 1 , p 2 , … , p n ) $(p_{1},p_{2},\ldots,p_{n})$ -Laplacian | Partial Differential Equations | p | Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | HEMIVARIATIONAL INEQUALITIES | EIGENVALUE PROBLEMS | Locally Lipschitz (p(1,) p . . . p(n))-Laplacian | NONTRIVIAL SOLUTIONS

Multiple solutions | Ordinary Differential Equations | Nonsmooth critical point | Variational methods | Locally Lipschitz | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | ( p 1 , p 2 , … , p n ) $(p_{1},p_{2},\ldots,p_{n})$ -Laplacian | Partial Differential Equations | p | Laplacian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | HEMIVARIATIONAL INEQUALITIES | EIGENVALUE PROBLEMS | Locally Lipschitz (p(1,) p . . . p(n))-Laplacian | NONTRIVIAL SOLUTIONS

Journal Article

IEEE Transactions on Robotics, ISSN 1552-3098, 08/2007, Volume 23, Issue 4, pp. 693 - 703

This paper addresses the connectedness issue in multiagent coordination, i.e., the problem of ensuring that a group of mobile agents stays connected while...

Multiagent systems | Protocols | Laplace equations | Control systems | History | multiagent coordination | formation control | Convergence | Connected graphs | Mobile agents | Distributed control | Autonomous agents | graph Laplacian | Multiagent coordination | Formation control | Graph laplacian | ROBOTICS | connected graphs | STABILITY | MOBILE AUTONOMOUS AGENTS | Analysis | Agents (artificial intelligence) | Dynamic tests | Dynamics | Graphs | Dynamical systems | Preserving

Multiagent systems | Protocols | Laplace equations | Control systems | History | multiagent coordination | formation control | Convergence | Connected graphs | Mobile agents | Distributed control | Autonomous agents | graph Laplacian | Multiagent coordination | Formation control | Graph laplacian | ROBOTICS | connected graphs | STABILITY | MOBILE AUTONOMOUS AGENTS | Analysis | Agents (artificial intelligence) | Dynamic tests | Dynamics | Graphs | Dynamical systems | Preserving

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 12/2014, Volume 76, Issue 11, pp. 855 - 874

SUMMARYIn this paper, we present LDG methods for systems with (p,δ)‐structure. The unknown gradient and the nonlinear diffusivity function are introduced as...

Newton–Picard iterative methods | (p,δ)‐structure system of equations | numerical solutions in domains with non‐smooth boundary | (p,δ)‐structure penalty jump terms | local discontinuous Galerkin methods | (p,δ)-structure system of equations | Newton-Picard iterative methods | (p,δ)-structure penalty jump terms | Numerical solutions in domains with non-smooth boundary | Local discontinuous Galerkin methods | APPROXIMATION | structure system of equations | PHYSICS, FLUIDS & PLASMAS | UNIFIED ANALYSIS | NONLINEAR DIFFUSION-PROBLEMS | ELLIPTIC PROBLEMS | ORDER | P-LAPLACIAN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | structure penalty jump terms | MESH REFINEMENT | numerical solutions in domains with non-smooth boundary | Mathematical analysis | Nonlinearity | Mathematical models | Runge-Kutta method | Boundaries | Fluxes | Iterative methods | Galerkin methods

Newton–Picard iterative methods | (p,δ)‐structure system of equations | numerical solutions in domains with non‐smooth boundary | (p,δ)‐structure penalty jump terms | local discontinuous Galerkin methods | (p,δ)-structure system of equations | Newton-Picard iterative methods | (p,δ)-structure penalty jump terms | Numerical solutions in domains with non-smooth boundary | Local discontinuous Galerkin methods | APPROXIMATION | structure system of equations | PHYSICS, FLUIDS & PLASMAS | UNIFIED ANALYSIS | NONLINEAR DIFFUSION-PROBLEMS | ELLIPTIC PROBLEMS | ORDER | P-LAPLACIAN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | structure penalty jump terms | MESH REFINEMENT | numerical solutions in domains with non-smooth boundary | Mathematical analysis | Nonlinearity | Mathematical models | Runge-Kutta method | Boundaries | Fluxes | Iterative methods | Galerkin methods

Journal Article

IEEE Transactions on Industrial Electronics, ISSN 0278-0046, 07/2012, Volume 59, Issue 7, pp. 3026 - 3041

This paper presents three design techniques for cooperative control of multiagent systems on directed graphs, namely, Lyapunov design, neural adaptive design,...

Laplace equations | Multiagent systems | Regulators | cooperative control | Laplacian potential | neural adaptive control | optimal control | Eigenvalues and eigenfunctions | Synchronization | Consensus | Lyapunov methods | multiagent system | CONSENSUS PROBLEMS | MULTIAGENT SYSTEMS | COORDINATION | DELAYS | NETWORKS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | PASSIVITY | MULTIVEHICLE SYSTEMS | AGENTS | AUTOMATION & CONTROL SYSTEMS | Measurement | Liapunov functions | Usage | Neural networks | Voltage | Design and construction | Mathematical optimization | Simulation methods | Multi-agent systems | Studies | Algorithms | Design engineering | Nonlinear dynamics | Cooperative control | Graphs | Graph theory | Tracking control | Adaptive control | Dynamical systems

Laplace equations | Multiagent systems | Regulators | cooperative control | Laplacian potential | neural adaptive control | optimal control | Eigenvalues and eigenfunctions | Synchronization | Consensus | Lyapunov methods | multiagent system | CONSENSUS PROBLEMS | MULTIAGENT SYSTEMS | COORDINATION | DELAYS | NETWORKS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | PASSIVITY | MULTIVEHICLE SYSTEMS | AGENTS | AUTOMATION & CONTROL SYSTEMS | Measurement | Liapunov functions | Usage | Neural networks | Voltage | Design and construction | Mathematical optimization | Simulation methods | Multi-agent systems | Studies | Algorithms | Design engineering | Nonlinear dynamics | Cooperative control | Graphs | Graph theory | Tracking control | Adaptive control | Dynamical systems

Journal Article

IET Control Theory & Applications, ISSN 1751-8644, 11/2017, Volume 11, Issue 16, pp. 2743 - 2752

This study is concerned with the robust adaptive backstepping control for hierarchical multi-agent systems with signed weights and non-linear system...

Research Article | hierarchical multiagent system stability | multi-agent systems | graph theory | hierarchical multivehicle systems | robust adaptive backstepping control scheme | TRACKING CONTROL | network model | control nonlinearities | robust control | Laplacian matrix | ANTAGONISTIC INTERACTIONS | nonlinear system uncertainties | stability | AUTOMATION & CONTROL SYSTEMS | INTERCONNECTED NONLINEAR-SYSTEMS | system uncertainties | controlled Laplacian | CONSENSUS PROBLEMS | uncertain systems | adaptive control | nonnegative weights | hierarchical systems | matrix algebra | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | SWITCHING TOPOLOGIES | nonlinear control systems | COMPLEX DYNAMICAL NETWORK | signed weights | recovery Laplacian

Research Article | hierarchical multiagent system stability | multi-agent systems | graph theory | hierarchical multivehicle systems | robust adaptive backstepping control scheme | TRACKING CONTROL | network model | control nonlinearities | robust control | Laplacian matrix | ANTAGONISTIC INTERACTIONS | nonlinear system uncertainties | stability | AUTOMATION & CONTROL SYSTEMS | INTERCONNECTED NONLINEAR-SYSTEMS | system uncertainties | controlled Laplacian | CONSENSUS PROBLEMS | uncertain systems | adaptive control | nonnegative weights | hierarchical systems | matrix algebra | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INSTRUMENTS & INSTRUMENTATION | SWITCHING TOPOLOGIES | nonlinear control systems | COMPLEX DYNAMICAL NETWORK | signed weights | recovery Laplacian

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 07/2017, Volume 158, pp. 109 - 131

This paper deals with the existence of nontrivial nonnegative solutions of Schrödinger–Hardy systems driven by two possibly different fractional ℘-Laplacian...

Fractional [formula omitted]-Laplacian operator | Schrödinger–Hardy systems | Existence of entire solutions | MATHEMATICS, APPLIED | MULTIPLICITY | CRITICAL NONLINEARITIES | Schrodinger-Hardy systems | MATHEMATICS | P-LAPLACIAN | SOBOLEV SPACES | R-N | Fractional p-Laplacian operator | R(N) | THEOREMS | UNBOUNDED-DOMAINS | AMBROSETTI-RABINOWITZ CONDITION | KIRCHHOFF EQUATIONS

Fractional [formula omitted]-Laplacian operator | Schrödinger–Hardy systems | Existence of entire solutions | MATHEMATICS, APPLIED | MULTIPLICITY | CRITICAL NONLINEARITIES | Schrodinger-Hardy systems | MATHEMATICS | P-LAPLACIAN | SOBOLEV SPACES | R-N | Fractional p-Laplacian operator | R(N) | THEOREMS | UNBOUNDED-DOMAINS | AMBROSETTI-RABINOWITZ CONDITION | KIRCHHOFF EQUATIONS

Journal Article

15.
Full Text
Generalised solutions for fully nonlinear PDE systems and existence–uniqueness theorems

Journal of Differential Equations, ISSN 0022-0396, 07/2017, Volume 263, Issue 1, pp. 641 - 686

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as...

Young measures | Generalised solutions | Baire Category method | Laplacian | Fully nonlinear systems | Campanato's near operators | SINGULAR SOLUTIONS | MATHEMATICS | MAPS | infinity-Laplacian | EQUATION | MINIMIZATION PROBLEMS

Young measures | Generalised solutions | Baire Category method | Laplacian | Fully nonlinear systems | Campanato's near operators | SINGULAR SOLUTIONS | MATHEMATICS | MAPS | infinity-Laplacian | EQUATION | MINIMIZATION PROBLEMS

Journal Article

Automatica, ISSN 0005-1098, 06/2019, Volume 104, pp. 17 - 25

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is...

Balanced truncation | Laplacian matrix | Network topology | Model reduction | Passivity | MULTIAGENT SYSTEMS | CONSENSUS | MODEL-REDUCTION | To be checked by Faculty | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Control systems | Analysis

Balanced truncation | Laplacian matrix | Network topology | Model reduction | Passivity | MULTIAGENT SYSTEMS | CONSENSUS | MODEL-REDUCTION | To be checked by Faculty | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Control systems | Analysis

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 08/2019, Volume 368, pp. 119 - 136