Number and profile of low energy solutions for singularly perturbed Klein-Gordon-Maxwell systems on a Riemannian manifold

DOI10.1016/j.jde.2014.01.012zbMath1286.58011arXiv1303.6498OpenAlexW2592340514MaRDI QIDQ2438111

Anna Maria Micheletti, Marco Ghimenti

Publication date: 10 March 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6498

zbMATH Keywords

Riemannian manifoldsSchrödinger-Maxwell systemsKlein-Gordon-Maxwell systemsLusternik Schnirelmann categoryone peak solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Variational principles in infinite-dimensional spaces (58E30) Electromagnetic interaction; quantum electrodynamics (81V10) Applications of PDEs on manifolds (58J90)

Related Items (13)

Existence of ground state solutions for the Schrödinger-Poisson systems ⋮ Schrödinger-Maxwell systems on non-compact Riemannian manifolds ⋮ A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in \(\mathbb{R}^N\) ⋮ Positive solutions for double singularly perturbed Schrödinger Maxwell systems ⋮ Boundary layers to a singularly perturbed Klein-Gordon-Maxwell-Proca system on a compact Riemannian manifold with boundary ⋮ Multiple solutions for a Schrödinger–Bopp–Podolsky system with positive potentials ⋮ The role of the scalar curvature in some singularly perturbed coupled elliptic systems on Riemannian manifolds ⋮ A multiplicity result for double singularly perturbed elliptic systems ⋮ Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary ⋮ Multiplicity results for the fractional Laplacian in expanding domains ⋮ Multiple solutions and profile description for a nonlinear Schrödinger-Bopp-Podolsky-Proca system on a manifold ⋮ Klein-Gordon-Maxwell equations in high dimensions ⋮ Low energy solutions for singularly perturbed coupled nonlinear systems on a Riemannian manifold with boundary

Cites Work

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• Dirichlet and Neumann problems for Klein-Gordon-Maxwell systems
• Multiple positive solutions for a Schrödinger-Poisson-Slater system
• On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations
• Ground state solutions for the nonlinear Schrödinger-Maxwell equations
• On the Schrödinger-Maxwell equations under the effect of a general nonlinear term
• The Klein-Gordon-Maxwell nonlinear system of equations
• Solution globale des équations de Maxwell-Dirac-Klein-Gordon
• An eigenvalue problem for the Schrödinger-Maxwell equations
• On the Maxwell-Klein-Gordon equation with finite energy
• Uniqueness of finite energy solutions for Maxwell-Dirac and Maxwell-Klein-Gordon equations
• Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with Maxwell's equations
• Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations
• Note on a Schrödinger-Poisson system in a bounded domain
• The role of the scalar curvature in some singularly perturbed coupled elliptic systems on Riemannian manifolds
• On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds
• Positive solution for a nonlinear stationary Schrödinger-Poisson system in \(\mathbb R^3\)
• Layered solutions for a semilinear elliptic system in a ball
• Clustered solutions around harmonic centers to a coupled elliptic system
• Klein-Gordon-Maxwell systems in a bounded domain
• Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
• EXISTENCE ANDA PRIORIBOUNDS FOR ELECTROSTATIC KLEIN–GORDON–MAXWELL SYSTEMS IN FULLY INHOMOGENEOUS SPACES
• MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM
• On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials
• SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS
• Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations
• Coupled Klein—Gordon and Born—Infeld-type equations: looking for solitary waves
• SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE

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