Concentration phenomenon of semiclassical states to reaction-diffusion systems

DOI10.1007/s10231-022-01297-5zbMath1520.35004arXiv1909.05453OpenAlexW4312222564MaRDI QIDQ6098123

Tian-Xiang Gou, Zhi-tao Zhang

Publication date: 12 June 2023

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05453

zbMATH Keywords

reaction-diffusion systemvariational methodssemiclassical statesconcentration phenomenon

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Variational methods for elliptic systems (35J50)

Related Items

Semi-classical states for elliptic system near saddle points of potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential
• Existence and concentration result for the Kirchhoff type equations with general nonlinearities
• An infinite-dimensional linking theorem without upper semi-continuous assumption and its applications
• Semi-classical states for the Choquard equation
• Existence of a nontrivial solution for a strongly indefinite periodic Choquard system
• Localized nodal solutions of higher topological type for semiclassical nonlinear Schrödinger equations
• Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential
• Homoclinic solutions of an infinite-dimensional Hamiltonian system
• Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials
• Periodic nonlinear Schrödinger equation with application to photonic crystals
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Existence and concentration of solitary waves for a class of quasilinear Schrödinger equations
• Ground state solutions for some indefinite variational problems
• On a class of nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Multi-peak bound states for nonlinear Schrödinger equations
• Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• On concentration of positive bound states of nonlinear Schrödinger equations
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• Generalized linking theorem with an application to a semilinear Schrödinger equation
• Effect of external potentials in a coupled system of multi-component incongruent diffusion
• Localized concentration of semi-classical states for nonlinear Dirac equations
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• An improved Fountain theorem and its application
• Localized nodal solutions for a critical nonlinear Schrödinger equation
• Solutions of a system of diffusion equations
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Concentrating patterns of reaction-diffusion systems: A variational approach
• Ground states of a system of nonlinear Schrödinger equations with periodic potentials
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Standing Waves for Nonlinear Schrodinger Equations with a General Nonlinearity: One and Two Dimensional Cases
• The chemical basis of morphogenesis

This page was built for publication: Concentration phenomenon of semiclassical states to reaction-diffusion systems