Journal of Differential Equations, ISSN 0022-0396, 04/2014, Volume 256, Issue 7, pp. 2449 - 2479

We consider a parametric nonlinear Robin problem driven by the p-Laplacian. We show that if the parameter λ>λˆ2= the second eigenvalue of the Robin...

Morse theory | Extremal solutions | Nonlinear regularity | Nonlinear maximum principle | Robin p-Laplacian | Nodal and constant sign solutions | MATHEMATICS | P-LAPLACIAN | ELLIPTIC-EQUATIONS | SPECTRUM | LOCAL MINIMIZERS

Morse theory | Extremal solutions | Nonlinear regularity | Nonlinear maximum principle | Robin p-Laplacian | Nodal and constant sign solutions | MATHEMATICS | P-LAPLACIAN | ELLIPTIC-EQUATIONS | SPECTRUM | LOCAL MINIMIZERS

Journal Article

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Multiplicity results for p-Laplacian boundary value problem with jumping nonlinearities

Boundary Value Problems, ISSN 1687-2762, 12/2019, Volume 2019, Issue 1, pp. 1 - 14

We investigate the multiplicity of solutions for one-dimensional p-Laplacian Dirichlet boundary value problem with jumping nonlinearities. We obtain three...

Jumping nonlinearity | 35J30 | 35A16 | 35J40 | 35J60 | 35A01 | p -Laplacian eigenvalue problem | Mathematics | p -Laplacian problem | Ordinary Differential Equations | Analysis | Contraction mapping principle | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Leray–Schauder degree theory | Partial Differential Equations | p-Laplacian problem | p-Laplacian eigenvalue problem | MATHEMATICS | Leray-Schauder degree theory | MATHEMATICS, APPLIED | Theorems | Boundary value problems | Eigenvalues | Dirichlet problem | Mapping | Eigenvectors | Eigen values

Jumping nonlinearity | 35J30 | 35A16 | 35J40 | 35J60 | 35A01 | p -Laplacian eigenvalue problem | Mathematics | p -Laplacian problem | Ordinary Differential Equations | Analysis | Contraction mapping principle | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Leray–Schauder degree theory | Partial Differential Equations | p-Laplacian problem | p-Laplacian eigenvalue problem | MATHEMATICS | Leray-Schauder degree theory | MATHEMATICS, APPLIED | Theorems | Boundary value problems | Eigenvalues | Dirichlet problem | Mapping | Eigenvectors | Eigen values

Journal Article

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 01/2016, Volume 33, Issue 1, pp. 93 - 118

Let Ω be a domain in Rn or a noncompact Riemannian manifold of dimension n≥2, and 1

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2016, Volume 290, pp. 376 - 391

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate...

Critical point theory | Existence and multiplicity | Weighted graph | [formula omitted]Laplacian on a graph | p(·)− Laplacian on a graph | MATHEMATICS, APPLIED | P-LAPLACIAN | GROWTH | EQUATIONS | NEUMANN PROBLEMS | P(.)-LAPLACIAN | p(center dot)-Laplacian on a graph

Critical point theory | Existence and multiplicity | Weighted graph | [formula omitted]Laplacian on a graph | p(·)− Laplacian on a graph | MATHEMATICS, APPLIED | P-LAPLACIAN | GROWTH | EQUATIONS | NEUMANN PROBLEMS | P(.)-LAPLACIAN | p(center dot)-Laplacian on a graph

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2018, Volume 468, Issue 1, pp. 324 - 343

In this paper, we consider the regularity of the weak solutions to a quasilinear parabolic systems which is a generalization of p-Laplacian of the...

Controllable growth condition | p-Laplacian | Moser-type iteration | Quasilinear parabolic systems | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | EQUATIONS | GRADIENTS | P-LAPLACIAN TYPE

Controllable growth condition | p-Laplacian | Moser-type iteration | Quasilinear parabolic systems | MATHEMATICS | MATHEMATICS, APPLIED | BEHAVIOR | EQUATIONS | GRADIENTS | P-LAPLACIAN TYPE

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

We study the extremal solutions of a class of fractional integro-differential equation with integral conditions on infinite intervals involving the p-Laplacian...

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

extremal solutions | monotone iterative method | fractional differential equation | Mathematics | 34B18 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | p -Laplacian operator | 34B40 | infinite intervals | Partial Differential Equations | p-Laplacian operator | MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | DIFFERENTIAL-EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | Infinite | Iterative methods (Mathematics) | Laplacian operator | Intervals | Operators | Approximation | Difference equations | Integrals | Mathematical analysis | Differential equations | Mathematical models | Iterative methods

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2016, Volume 195, Issue 6, pp. 2099 - 2129

The paper deals with existence, multiplicity and asymptotic behavior of entire solutions for a series of stationary Kirchhoff fractional p-Laplacian equations....

35J20 | 35J60 | 35R11 | Mathematics, general | Mathematics | Hardy coefficients | Stationary Kirchhoff problems | Critical exponents | 35B09 | Non-local p -Laplacian operators | Non-local p-Laplacian operators | MATHEMATICS | MATHEMATICS, APPLIED | R-N | MULTIPLICITY | OPERATOR | ELLIPTIC-EQUATIONS

35J20 | 35J60 | 35R11 | Mathematics, general | Mathematics | Hardy coefficients | Stationary Kirchhoff problems | Critical exponents | 35B09 | Non-local p -Laplacian operators | Non-local p-Laplacian operators | MATHEMATICS | MATHEMATICS, APPLIED | R-N | MULTIPLICITY | OPERATOR | ELLIPTIC-EQUATIONS

Journal Article

Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2016, Volume 2016, Issue 106, pp. 1 - 9

A new existence result is obtained for nonautonomous second order Hamiltonian systems with (q, p)-Laplacian by using the minimax methods.

Hamiltonian systems with (q P)-Laplacian | Periodic solutions | Saddle point theorem | Cerami condition | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Hamiltonian systems with (q, p)-Laplacian | periodic solutions | P-LAPLACIAN SYSTEMS | saddle point theorem | DIFFERENTIAL-SYSTEMS | cerami condition; saddle point theorem | p)$-laplacian | hamiltonian systems with $(q

Hamiltonian systems with (q P)-Laplacian | Periodic solutions | Saddle point theorem | Cerami condition | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Hamiltonian systems with (q, p)-Laplacian | periodic solutions | P-LAPLACIAN SYSTEMS | saddle point theorem | DIFFERENTIAL-SYSTEMS | cerami condition; saddle point theorem | p)$-laplacian | hamiltonian systems with $(q

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2017, Volume 2017, Issue 1, pp. 1 - 18

In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems...

Ordinary Differential Equations | positive solution | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | p -Laplacian operator | Mathematics | Partial Differential Equations | nonlocal boundary value problem | fractional differential system | p-Laplacian operator | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | COUPLED SYSTEM | UNIQUENESS | Nonlinear equations | Boundary value problems | Fixed points (mathematics) | Parameters | Differential equations

Ordinary Differential Equations | positive solution | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | p -Laplacian operator | Mathematics | Partial Differential Equations | nonlocal boundary value problem | fractional differential system | p-Laplacian operator | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | COUPLED SYSTEM | UNIQUENESS | Nonlinear equations | Boundary value problems | Fixed points (mathematics) | Parameters | Differential equations

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 12

In this paper, we investigate the existence and multiplicity of nontrivial weak solutions for a class of nonlinear impulsive (q, p)-Laplacian dynamical...

(q, p) -Laplacian | variational methods | existence | multiplicity | nontrivial solution | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | P-LAPLACIAN | 2ND-ORDER DIFFERENTIAL-SYSTEMS | EQUATIONS | (q, p)-Laplacian | Theorems (Mathematics) | Usage | Variational principles | Laplacian operator | Nonlinear systems | Dynamical systems | Critical point | ( q , p ) $(q,p)$ -Laplacian

(q, p) -Laplacian | variational methods | existence | multiplicity | nontrivial solution | MATHEMATICS | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | P-LAPLACIAN | 2ND-ORDER DIFFERENTIAL-SYSTEMS | EQUATIONS | (q, p)-Laplacian | Theorems (Mathematics) | Usage | Variational principles | Laplacian operator | Nonlinear systems | Dynamical systems | Critical point | ( q , p ) $(q,p)$ -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

IEEE Transactions on Image Processing, ISSN 1057-7149, 07/2008, Volume 17, Issue 7, pp. 1047 - 1060

We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach...

weighted graph | Smoothing methods | Filtering | p -Laplacian | Image processing | Noise reduction | nonlocal discrete regularization | Image and manifold processing | Topology | Data mining | Digital filters | Manifolds | Machine learning | p-Laplacian | Nonlocal discrete regularization | Weighted graph | regularization | nonlocal discrete | EQUATIONS | image and manifold processing | DIFFUSION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Reproducibility of Results | Algorithms | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Sensitivity and Specificity | Imaging, Three-Dimensional - methods | Signal Processing, Computer-Assisted | Image Enhancement - methods | Usage | Analysis | Graphic methods | Studies | Energy use | Television | Energy conservation | Images | Graphs | Regularization | Image Processing | Computer Science

weighted graph | Smoothing methods | Filtering | p -Laplacian | Image processing | Noise reduction | nonlocal discrete regularization | Image and manifold processing | Topology | Data mining | Digital filters | Manifolds | Machine learning | p-Laplacian | Nonlocal discrete regularization | Weighted graph | regularization | nonlocal discrete | EQUATIONS | image and manifold processing | DIFFUSION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Reproducibility of Results | Algorithms | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Sensitivity and Specificity | Imaging, Three-Dimensional - methods | Signal Processing, Computer-Assisted | Image Enhancement - methods | Usage | Analysis | Graphic methods | Studies | Energy use | Television | Energy conservation | Images | Graphs | Regularization | Image Processing | Computer Science

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2017, Volume 455, Issue 2, pp. 1470 - 1504

We deal with a nonlocal nonlinear evolution problem of the form∬Rn×RJ(x−y,t−s)|v‾(y,s)−v(x,t)|p−2(v‾(y,s)−v(x,t))dyds=0 for (x,t)∈Rn×[0,∞). Here p≥2, J:Rn+1→R...

p-Laplacian | Nonlocal evolution problems | Mean value properties | OF-WAR GAMES | MATHEMATICS | MATHEMATICS, APPLIED | FRACTIONAL P-LAPLACIAN

p-Laplacian | Nonlocal evolution problems | Mean value properties | OF-WAR GAMES | MATHEMATICS | MATHEMATICS, APPLIED | FRACTIONAL P-LAPLACIAN

Journal Article

IEEE Transactions on Cybernetics, ISSN 2168-2267, 08/2019, Volume 49, Issue 8, pp. 2927 - 2940

The explosive growth of multimedia data on the Internet makes it essential to develop innovative machine learning algorithms for practical applications...

Manifolds | Geometry | Laplace equations | Semisupervised learning | semi-supervised learning (SSL) | Approximation algorithms | Laplacian regularization (LapR) | scene recognition | Eigenvalues and eigenfunctions | Standards | p -Laplacian">p -Laplacian | manifold learning | p-Laplacian | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS

Manifolds | Geometry | Laplace equations | Semisupervised learning | semi-supervised learning (SSL) | Approximation algorithms | Laplacian regularization (LapR) | scene recognition | Eigenvalues and eigenfunctions | Standards | p -Laplacian">

Journal Article

Inverse Problems, ISSN 0266-5611, 01/2019, Volume 35, Issue 3, p. 35004

The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed...

nonlinear quasi-variational inequality | obstacle problem | p -Laplacian | inverse problems | regularization | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | HEMIVARIATIONAL INEQUALITIES | IDENTIFICATION | PHYSICS, MATHEMATICAL | VALUED EQUILIBRIUM PROBLEMS

nonlinear quasi-variational inequality | obstacle problem | p -Laplacian | inverse problems | regularization | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | HEMIVARIATIONAL INEQUALITIES | IDENTIFICATION | PHYSICS, MATHEMATICAL | VALUED EQUILIBRIUM PROBLEMS

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 3/2018, Volume 39, Issue 2, pp. 357 - 372

The authors study the following Dirichlet problem of a system involving fractional (p, q)-Laplacian operators: $$\left\{ {\begin{array}{*{20}{c}} {\left( { -...

Variational methods | 35A15 | 47G20 | The Nehari manifold | 35J60 | Fractional p -Laplacian | 35R11 | Mathematics, general | Mathematics | Applications of Mathematics | Fractional p-Laplacian | MATHEMATICS | P-LAPLACIAN | NEHARI MANIFOLD

Variational methods | 35A15 | 47G20 | The Nehari manifold | 35J60 | Fractional p -Laplacian | 35R11 | Mathematics, general | Mathematics | Applications of Mathematics | Fractional p-Laplacian | MATHEMATICS | P-LAPLACIAN | NEHARI MANIFOLD

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2020, Volume 43, Issue 2, pp. 968 - 995

In this paper, we study the existence of three solutions for a Kirchhoff equation involving the nonlocal fractional p‐Laplacian considering Sobolev and Hardy...

fractional p‐Laplacian | Kirchhoff problem | critical exponents | EXISTENCE | fractional p-Laplacian | MATHEMATICS, APPLIED | ENERGY | NONLOCAL PROBLEMS | EQUATION | Mountains

fractional p‐Laplacian | Kirchhoff problem | critical exponents | EXISTENCE | fractional p-Laplacian | MATHEMATICS, APPLIED | ENERGY | NONLOCAL PROBLEMS | EQUATION | Mountains

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 08/2017, Volume 263, Issue 3, pp. 1931 - 1945

We study the regularity of the free boundary in the obstacle for the p-Laplacian, min{−Δpu,u−φ}=0 in Ω⊂Rn. Here, Δpu=div(|∇u|p−2∇u), and p∈(1,2)∪(2,∞). Near...

p-Laplacian | Free boundary | Obstacle problem | MATHEMATICS

p-Laplacian | Free boundary | Obstacle problem | MATHEMATICS

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 8/2019, Volume 80, Issue 1, pp. 63 - 80

In this paper we study a class of critical Kirchhoff type equations involving the fractional p–Laplacian operator, that is $$\begin{aligned} \begin{array}{ll}...

Degenerate Kirchhoff equations | Variational methods | 35A15 | Systems Theory, Control | Critical Sobolev exponent | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics | 49J35 | Mathematical Methods in Physics | 47G20 | Calculus of Variations and Optimal Control; Optimization | 35R11 | Numerical and Computational Physics, Simulation | Fractional p –Laplacian | Fractional p–Laplacian | EXISTENCE | MATHEMATICS, APPLIED | THEOREM | Fractional p-Laplacian | EXPONENT | MULTIPLE POSITIVE SOLUTIONS

Degenerate Kirchhoff equations | Variational methods | 35A15 | Systems Theory, Control | Critical Sobolev exponent | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics | 49J35 | Mathematical Methods in Physics | 47G20 | Calculus of Variations and Optimal Control; Optimization | 35R11 | Numerical and Computational Physics, Simulation | Fractional p –Laplacian | Fractional p–Laplacian | EXISTENCE | MATHEMATICS, APPLIED | THEOREM | Fractional p-Laplacian | EXPONENT | MULTIPLE POSITIVE SOLUTIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2015, Volume 424, Issue 2, pp. 1021 - 1041

The purpose of this paper is to investigate the existence of weak solutions for a Kirchhoff type problem driven by a non-local integro-differential operator of...

Fractional p-Laplacian | Mountain Pass Theorem | Kirchhoff type problem | Integro-differential operator | Mountain pass theorem | INEQUALITIES DRIVEN | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | ELLIPTIC-OPERATORS

Fractional p-Laplacian | Mountain Pass Theorem | Kirchhoff type problem | Integro-differential operator | Mountain pass theorem | INEQUALITIES DRIVEN | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | ELLIPTIC-OPERATORS

Journal Article

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