Journal of mathematical fluid mechanics, ISSN 1422-6952, 2017, Volume 20, Issue 1, pp. 161 - 187

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation...

Mathematical Methods in Physics | Fluid- and Aerodynamics | Classical and Continuum Physics | Primary 35Q31 | Secondary 35B32 | 76B15 | Physics | 35C07 | STEADY | ANALYTICITY | GLOBAL BIFURCATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | REGULARITY | PHYSICS, FLUIDS & PLASMAS | STOKES WAVES | CONSTANT VORTICITY | MULTIPLE CRITICAL LAYERS | FLOWS | Water waves | Analysis

Mathematical Methods in Physics | Fluid- and Aerodynamics | Classical and Continuum Physics | Primary 35Q31 | Secondary 35B32 | 76B15 | Physics | 35C07 | STEADY | ANALYTICITY | GLOBAL BIFURCATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | REGULARITY | PHYSICS, FLUIDS & PLASMAS | STOKES WAVES | CONSTANT VORTICITY | MULTIPLE CRITICAL LAYERS | FLOWS | Water waves | Analysis

Journal Article

Archive for rational mechanics and analysis, ISSN 1432-0673, 2019, Volume 235, Issue 1, pp. 405 - 470

We study the existence of patterns (nontrivial, stationary solutions) in the onedimensional Swift-Hohenberg Equation in a directional quenching scenario, that...

PATTERN-FORMATION | MATHEMATICS, APPLIED | GRAIN-BOUNDARIES | DEFECTS | MECHANICS | INTERFACES | SYSTEMS | ANGLE | VALIDITY | BIFURCATION | Fourier analysis | Orbits | Decomposition | Quenching

PATTERN-FORMATION | MATHEMATICS, APPLIED | GRAIN-BOUNDARIES | DEFECTS | MECHANICS | INTERFACES | SYSTEMS | ANGLE | VALIDITY | BIFURCATION | Fourier analysis | Orbits | Decomposition | Quenching

Journal Article

Nonlinear dynamics, ISSN 0924-090X, 2019, Volume 97, Issue 1, pp. 571 - 582

This paper presents necessary and sufficient conditions for the existence of bright/dark solitary solutions in the Hodgkin-Huxley model. The second-order...

Hodgkin-Huxley model | MECHANICS | EXP-FUNCTION | Heteroclinic bifurcation | 35B32 | NEURONS | Generalized differential operator | Solitary solution | 35C08 | DESYNCHRONIZATION | ENGINEERING, MECHANICAL | Operators (mathematics) | Economic models | Broken symmetry | Saddle points | Differential equations | Bifurcations | Trajectories | Symmetry

Hodgkin-Huxley model | MECHANICS | EXP-FUNCTION | Heteroclinic bifurcation | 35B32 | NEURONS | Generalized differential operator | Solitary solution | 35C08 | DESYNCHRONIZATION | ENGINEERING, MECHANICAL | Operators (mathematics) | Economic models | Broken symmetry | Saddle points | Differential equations | Bifurcations | Trajectories | Symmetry

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 2018, Volume 19, Issue 2, pp. 391 - 412

We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights,...

Concave-Convex Problem | Positive Solution | Loop Bifurcation | Indefinite Nonlinearity | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL SUPERLINEARITY | FIXED-POINT EQUATIONS

Concave-Convex Problem | Positive Solution | Loop Bifurcation | Indefinite Nonlinearity | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL SUPERLINEARITY | FIXED-POINT EQUATIONS

Journal Article

Calculus of variations and partial differential equations, ISSN 1432-0835, 2009, Volume 37, Issue 3-4, pp. 345 - 361

The paper is concerned with the local and global bifurcation structure of positive solutions $${u,v\in H^1_0(\Omega)}$$ of the system...

35B05 | 35J50 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 35B32 | 58C40 | Mathematics | 58E07 | 35J55 | MATHEMATICS | COUPLED SCHRODINGER-EQUATIONS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | STATES | SOLITARY WAVES | ANNULUS | SPIKES | POTENTIALS | UNIQUENESS | Mathematical analysis | Bifurcations | Nonlinearity | Bifurcation theory | Joining | Schroedinger equation | Spectra | Nonlinear optics

35B05 | 35J50 | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 35B32 | 58C40 | Mathematics | 58E07 | 35J55 | MATHEMATICS | COUPLED SCHRODINGER-EQUATIONS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | R-N | STATES | SOLITARY WAVES | ANNULUS | SPIKES | POTENTIALS | UNIQUENESS | Mathematical analysis | Bifurcations | Nonlinearity | Bifurcation theory | Joining | Schroedinger equation | Spectra | Nonlinear optics

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2019, Volume 58, Issue 1, pp. 1 - 23

In the paper the asymptotic bifurcation of solutions to a parameterized stationary semilinear Schrödinger equation involving a potential of the Kato-Rellich...

37B30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J | 35B32 | 35K | Mathematics

37B30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J | 35B32 | 35K | Mathematics

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 2016, Volume 289, Issue 2-3, pp. 332 - 342

We prove a bifurcation and multiplicity result for a critical fractional p‐Laplacian problem that is the analog of the Brézis‐Nirenberg problem for the...

bifurcation | 58E05 | critical nonlinearity | 35B33 | 35B32 | 35R11 | pseudo‐index | cohomological index | Fractional p‐Laplacian | Bifurcation | Fractional p-Laplacian | Pseudo-index | Cohomological index | Critical nonlinearity | pseudo-index | EIGENVALUE | EXISTENCE | POSITIVE SOLUTIONS | BREZIS-NIRENBERG RESULT | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL SOBOLEV EXPONENTS | FUNCTIONALS

bifurcation | 58E05 | critical nonlinearity | 35B33 | 35B32 | 35R11 | pseudo‐index | cohomological index | Fractional p‐Laplacian | Bifurcation | Fractional p-Laplacian | Pseudo-index | Cohomological index | Critical nonlinearity | pseudo-index | EIGENVALUE | EXISTENCE | POSITIVE SOLUTIONS | BREZIS-NIRENBERG RESULT | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL SOBOLEV EXPONENTS | FUNCTIONALS

Journal Article

ADVANCED NONLINEAR STUDIES, ISSN 1536-1365, 11/2019, Volume 19, Issue 4, pp. 757 - 770

We consider the Henon problem {-Delta u = vertical bar x vertical bar(alpha)u(N+2+2 alpha/N-2-epsilon )in B-1, u > 0 in B-1, u = 0 on partial derivative B-1,...

Henon Problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Bifurcation | DOMAINS | Nonradial Solutions | SYMMETRY-BREAKING

Henon Problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Bifurcation | DOMAINS | Nonradial Solutions | SYMMETRY-BREAKING

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 1/2017, Volume 108, Issue 1, pp. 71 - 83

We study the solution $${u(r,\rho)}$$ u ( r , ρ ) of the quasilinear elliptic problem $$\begin{cases}...

Secondary 35C10 | Singular solutions | Intersection number | 35B32 | Mathematics, general | Mathematics | 70K05 | Quasilinear elliptic equation | Radial solutions | Primary 35B05 | MATHEMATICS

Secondary 35C10 | Singular solutions | Intersection number | 35B32 | Mathematics, general | Mathematics | 70K05 | Quasilinear elliptic equation | Radial solutions | Primary 35B05 | MATHEMATICS

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2019, Volume 70, Issue 4, pp. 1 - 13

We study a superlinear and subcritical Kirchhoff-type equation which is variational and depends upon a real parameter $$\lambda $$ λ . The nonlocal term forces...

Young’s modulus | Engineering | Mathematical Methods in Physics | Nehari Manifold | Variational methods | 35A15 | Kirchhoff | 35B32 | Stiffness | Primary 35A02 | Theoretical and Applied Mechanics | Extremal parameter | Mathematics - Analysis of PDEs

Young’s modulus | Engineering | Mathematical Methods in Physics | Nehari Manifold | Variational methods | 35A15 | Kirchhoff | 35B32 | Stiffness | Primary 35A02 | Theoretical and Applied Mechanics | Extremal parameter | Mathematics - Analysis of PDEs

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 11/2017, Volume 290, Issue 16, pp. 2597 - 2611

In this paper, we consider the bifurcation problem for the fractional Laplace equation (−Δ)su=λu+f(λ,x,u)inΩ,u=0inRn∖Ω,where Ω⊂Rn,n>2s(0~~ bifurcation | Variational methods | 35A15 | 47G20 | fractional Laplacian | 35B32 | integrodifferential operators | OBSTACLE PROBLEM | MATHEMATICS | EIGENVALUES | P-LAPLACIAN | REGULARITY | FREE-BOUNDARY ~~

Journal Article

Communications in partial differential equations, ISSN 1532-4133, 2015, Volume 40, Issue 5, pp. 918 - 956

Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations...

Network formation | Stability | Weak solutions | Energy dissipation | Bifurcation analysis | MATHEMATICS | MATHEMATICS, APPLIED | 92C42 | MEAN-OSCILLATION | 35B32 | 35K55 | Market analysis | Business incubators | Environmental protection | Partial differential equations | Dynamics | Mathematical analysis | Mathematical models | Conductance | Dynamical systems | Steady state

Network formation | Stability | Weak solutions | Energy dissipation | Bifurcation analysis | MATHEMATICS | MATHEMATICS, APPLIED | 92C42 | MEAN-OSCILLATION | 35B32 | 35K55 | Market analysis | Business incubators | Environmental protection | Partial differential equations | Dynamics | Mathematical analysis | Mathematical models | Conductance | Dynamical systems | Steady state

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 26

In this paper we establish existence of radial and nonradial solutions to the system $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u_1 =...

Primary 35J47 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35B32 | Secondary 35B09 | Mathematics | 35B08 | MATHEMATICS | MATHEMATICS, APPLIED | ELLIPTIC SYSTEM

Primary 35J47 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35B32 | Secondary 35B09 | Mathematics | 35B08 | MATHEMATICS | MATHEMATICS, APPLIED | ELLIPTIC SYSTEM

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 15

This paper investigates the stability of bifurcating steady states of a spatially heterogeneous cooperative system with cross-diffusion. According to the...

Ordinary Differential Equations | Functional Analysis | 35B35 | Analysis | Difference and Functional Equations | 35B32 | Mathematics, general | spectral analysis | Mathematics | Partial Differential Equations | stability | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | INSTABILITY | MODEL

Ordinary Differential Equations | Functional Analysis | 35B35 | Analysis | Difference and Functional Equations | 35B32 | Mathematics, general | spectral analysis | Mathematics | Partial Differential Equations | stability | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | INSTABILITY | MODEL

Journal Article

15.
Full Text
Rich spatial–temporal dynamics in a diffusive population model for pioneer–climax species

Nonlinear Dynamics, ISSN 0924-090X, 2/2019, Volume 95, Issue 3, pp. 1731 - 1745

A general diffusive population model for interactions of pioneer and climax species subject to the no-flux boundary condition is considered. Local and global...

Spatial–temporal pattern | Climax species | Classical Mechanics | 35K57 | Engineering | Vibration, Dynamical Systems, Control | 92B05 | 92D25 | Turing bifurcation | 35B32 | Automotive Engineering | Mechanical Engineering | Pioneer species | Diffusion | Hopf bifurcation | MECHANICS | Spatial-temporal pattern | ENGINEERING, MECHANICAL | Analysis | Models | Numerical analysis

Spatial–temporal pattern | Climax species | Classical Mechanics | 35K57 | Engineering | Vibration, Dynamical Systems, Control | 92B05 | 92D25 | Turing bifurcation | 35B32 | Automotive Engineering | Mechanical Engineering | Pioneer species | Diffusion | Hopf bifurcation | MECHANICS | Spatial-temporal pattern | ENGINEERING, MECHANICAL | Analysis | Models | Numerical analysis

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 11/2018, Volume 18, Issue 4, pp. 845 - 862

The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on...

Non-cooperative Elliptic Systems | Symmetric Rabinowitz Alternative | Equivariant Degree | Global Symmetry-Breaking Bifurcations | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BIFURCATION

Non-cooperative Elliptic Systems | Symmetric Rabinowitz Alternative | Equivariant Degree | Global Symmetry-Breaking Bifurcations | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BIFURCATION

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1

We consider the stationary Keller-Segel equation {-Lambda v + v = lambda e(v), v > 0 in Omega, partial derivative(nu)v = 0 on partial derivative Omega, where...

35B32 | 35B05 | 35B40 | 35B25 | 35J25 | 35B09 | MATHEMATICS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | PERTURBED NEUMANN PROBLEM | STEADY-STATES | CHEMOTAXIS | BEHAVIOR | Analysis of PDEs | Mathematics

35B32 | 35B05 | 35B40 | 35B25 | 35J25 | 35B09 | MATHEMATICS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | PERTURBED NEUMANN PROBLEM | STEADY-STATES | CHEMOTAXIS | BEHAVIOR | Analysis of PDEs | Mathematics

Journal Article

Journal of mathematical biology, ISSN 1432-1416, 2018, Volume 78, Issue 3, pp. 655 - 682

Hyperbolic transport-reaction equations are abundant in the description of movement of motile organisms. Here, we focus on a system of four coupled...

Wave formation | Viscous limit | Pattern formation | 35L60 | 35B36 | Mathematical and Computational Biology | 35B35 | 34D20 | Hyperbolic equations | Traveling waves | Mathematics | Myxobacteria | 35Q70 | 92D25 | 35B32 | 35B65 | Applications of Mathematics | Age-structured equations | 35B40 | 92D50 | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | DIFFUSION | AGGREGATION | Usage | Wave propagation | Analysis | Equations | Mathematical models | Stability analysis | Transport | Age

Wave formation | Viscous limit | Pattern formation | 35L60 | 35B36 | Mathematical and Computational Biology | 35B35 | 34D20 | Hyperbolic equations | Traveling waves | Mathematics | Myxobacteria | 35Q70 | 92D25 | 35B32 | 35B65 | Applications of Mathematics | Age-structured equations | 35B40 | 92D50 | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | DIFFUSION | AGGREGATION | Usage | Wave propagation | Analysis | Equations | Mathematical models | Stability analysis | Transport | Age

Journal Article

19.
Full Text
Positive solutions of Kirchhoff-type non-local elliptic equation: a bifurcation approach

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 08/2017, Volume 147, Issue 4, pp. 875 - 894

Positive solutions of a Kirchhoff-type nonlinear elliptic equation with a non-local integral term on a bounded domain in ℝ N , N ⩾ 1, are studied by using...

35J62 | 35J25 | 2010 Mathematics subject classification: Primary 35J60 | Secondary 35B32 | EXISTENCE | GLOBAL SOLVABILITY | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | MULTIPLICITY | BEHAVIOR | NONTRIVIAL SOLUTIONS | bifurcation theory | UNIQUENESS | Kirchhoff-type equation | MATHEMATICS | positive solution | CRITICAL GROWTH | R-3 | DOMAINS | Eigenvalues | Bifurcation theory | Uniqueness | Eigen values

35J62 | 35J25 | 2010 Mathematics subject classification: Primary 35J60 | Secondary 35B32 | EXISTENCE | GLOBAL SOLVABILITY | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | MULTIPLICITY | BEHAVIOR | NONTRIVIAL SOLUTIONS | bifurcation theory | UNIQUENESS | Kirchhoff-type equation | MATHEMATICS | positive solution | CRITICAL GROWTH | R-3 | DOMAINS | Eigenvalues | Bifurcation theory | Uniqueness | Eigen values

Journal Article

Journal of mathematical biology, ISSN 0303-6812, 2012, Volume 66, Issue 6, pp. 1241 - 1266

The most important phenomenon in chemotaxis is cell aggregation. To model this phenomenon we use spiky or transition layer (step-function-like) steady states....

Mathematical and Computational Biology | 35B32 | Mathematics | 92C17 | 35B41 | Applications of Mathematics | 26A48 | 35J67 | EXISTENCE | STABILITY | STATIONARY SOLUTIONS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | PATTERNS | KELLER-SEGEL MODEL | AGGREGATION | Mathematical Concepts | Chemotaxis - physiology | Models, Biological | Cell Aggregation - physiology | Bifurcation theory | Research | Biomathematics | Chemotaxis

Mathematical and Computational Biology | 35B32 | Mathematics | 92C17 | 35B41 | Applications of Mathematics | 26A48 | 35J67 | EXISTENCE | STABILITY | STATIONARY SOLUTIONS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | PATTERNS | KELLER-SEGEL MODEL | AGGREGATION | Mathematical Concepts | Chemotaxis - physiology | Models, Biological | Cell Aggregation - physiology | Bifurcation theory | Research | Biomathematics | Chemotaxis

Journal Article

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