On the existence and shape of least energy solutions for some elliptic systems.

DOI10.1016/S0022-0396(03)00017-2zbMath1109.35325OpenAlexW2061832659MaRDI QIDQ1399895

Jianfu Yang, Andrés I. Ávila

Publication date: 30 July 2003

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

Full work available at URL: https://doi.org/10.1016/s0022-0396(03)00017-2

zbMATH Keywords

positive solutionselliptic systemsemilinearIndefinite

Mathematics Subject Classification ID

Related Items (49)

Locating the peaks of the least energy solutions to an elliptic system with Neumann boundary conditions ⋮ Existence of solutions for perturbed elliptic system with critical exponents ⋮ On ground state solutions for superlinear Hamiltonian elliptic systems ⋮ Ground-state solutions for superquadratic Hamiltonian elliptic systems with gradient terms ⋮ Local mountain pass for a class of elliptic system ⋮ Existence of solutions for nonperiodic superquadratic Hamiltonian elliptic systems ⋮ Solutions for a class of nonperiodic superquadratic Hamiltonian elliptic systems involving gradient terms ⋮ Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type ⋮ The existence of solutions for superquadratic Hamiltonian elliptic systems on \(\mathbb R^N\) ⋮ Existence and multiplicity of semiclassical solutions for asymptotically Hamiltonian elliptic systems ⋮ Semiclassical limits of ground states for Hamiltonian elliptic system with gradient term ⋮ Semi-classical states for elliptic system near saddle points of potentials ⋮ Concentration results for a singularly perturbed elliptic system with variable coefficients ⋮ Multiple solutions for a superlinear and periodic elliptic system on \({\mathbb{R}^N}\) ⋮ Ground state solutions of Nehari-Pankov type for a superlinear elliptic system on RN ⋮ Concentration behavior of semiclassical solutions for Hamiltonian elliptic system ⋮ Ground states and multiple solutions for Hamiltonian elliptic system with gradient term ⋮ Multiplicity of semiclassical solutions for a class of nonlinear Hamiltonian elliptic system ⋮ Nontrivial solutions for a class of Hamiltonian strongly degenerate elliptic system ⋮ Existence and concentration of semiclassical solutions for Hamiltonian elliptic system ⋮ Existence of nontrivial solutions for perturbed elliptic system in \(\mathbb{R}^N\) ⋮ Existence and concentration properties of ground state solutions for elliptic systems ⋮ Semiclassical limits of ground state solutions to Schrödinger systems ⋮ Semi-classical solutions of perturbed elliptic system with general superlinear nonlinearity ⋮ Solutions with multiple spike patterns for an elliptic system ⋮ Super-critical Neumann problems on unbounded domains ⋮ Ground state solutions for Hamiltonian elliptic system with inverse square potential ⋮ The estimates on the energy functional of an elliptic system with Neumann boundary conditions ⋮ Existence and multiplicity of solutions for asymptotically Hamiltonian elliptic systems in \(\mathbb R^N\) ⋮ Hamiltonian elliptic systems: a guide to variational frameworks ⋮ A note on superlinear Hamiltonian elliptic systems ⋮ Infinitely many solutions for superlinear periodic Hamiltonian elliptic systems ⋮ Spike-layered solutions for an elliptic system with Neumann boundary conditions ⋮ Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems ⋮ Existence and asymptotic behavior of ground states for Schrödinger systems with Hardy potential ⋮ Multiple solutions of a coupled nonlinear Schrödinger system ⋮ Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions ⋮ Multiplicity of positive solutions for a mixed boundary elliptic system ⋮ On singular perturbations of superlinear elliptic systems ⋮ Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems ⋮ Ground states for planar Hamiltonian elliptic systems with critical exponential growth ⋮ Existence and decay property of ground state solutions for Hamiltonian elliptic system ⋮ Semiclassical states for coupled nonlinear Schrödinger system with competing potentials ⋮ Singularly perturbed elliptic systems ⋮ On semiclassical ground state solutions for Hamiltonian elliptic systems ⋮ Multiple solutions for a semilinear elliptic system in RN ⋮ Nontrivial solutions for an elliptic system of Hamiltonian type ⋮ Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity ⋮ Existence of solutions for periodic elliptic system with general superlinear nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Initiation of slime mold aggregation viewed as an instability
• Large amplitude stationary solutions to a chemotaxis system
• Locating the peaks of least-energy solutions to a semilinear Neumann problem
• Differential systems with strongly indefinite variational structure
• Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity
• On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Decay, symmetry and existence of solutions of semilinear elliptic systems
• On Superquadratic Elliptic Systems
• Strongly indefinite systems with critical Sobolev exponents
• Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting
• On the existence of solutions of Hamiltonian elliptic systems in \(\mathbb{R}^N\).

This page was built for publication: On the existence and shape of least energy solutions for some elliptic systems.