Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with \(d\geq 3\) equations

DOI10.1016/j.jfa.2016.06.017zbMath1351.35046arXiv1508.01783OpenAlexW2963095490MaRDI QIDQ306563

Filipe Oliveira, Simão Correia, Hugo Tavares

Publication date: 31 August 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.01783

zbMATH Keywords

weak solutionsground statescubic Schrödinger systems of cooperative typegradient elliptic systemssemitrivial and fully nontrivial solutions

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) NLS equations (nonlinear Schrödinger equations) (35Q55) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09) Entire solutions to PDEs (35B08)

Related Items

Ground states for a nonlinear Schrödinger system with sublinear coupling terms ⋮ Classification of ground-states of a coupled Schrödinger system ⋮ Least energy positive solutions of critical Schrödinger systems with mixed competition and cooperation terms: the higher dimensional case ⋮ Spiked vector solutions of coupled Schrödinger systems with critical exponent and solutions concentrating on spheres ⋮ Ground states of nonlinear Schrödinger systems with mixed couplings: the critical case ⋮ Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems ⋮ Ground states of nonlinear Schrödinger systems with mixed couplings ⋮ Infinitely many nonradial positive solutions for multi-species nonlinear Schrödinger systems in \(\mathbb{R}^N\) ⋮ Least energy positive solutions for \(d\)-coupled Schrödinger systems with critical exponent in dimension three ⋮ Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions ⋮ Positive vector solutions for nonlinear Schrödinger systems with strong interspecies attractive forces ⋮ Spiked solutions for Schrödinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions ⋮ Existence of least energy positive solutions to Schrödinger systems with mixed competition and cooperation terms: the critical case ⋮ Positive ground states for coupled nonlinear Choquard equations involving Hardy-Littlewood-Sobolev critical exponent ⋮ Positive least energy solutions for coupled nonlinear Choquard equations with Hardy-Littlewood-Sobolev critical exponent

Cites Work

• Unnamed Item
• New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms
• Ground-states for systems of \(M\) coupled semilinear Schrödinger equations with attraction-repulsion effects: characterization and perturbation results
• Ground states for a nonlinear Schrödinger system with sublinear coupling terms
• Note on ground states of a nonlinear Schrödinger system
• Partial symmetry of vector solutions for elliptic systems
• Positive solutions to some systems of coupled nonlinear Schrödinger equations
• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Characterization of ground-states for a system of \(M\) coupled semilinear Schrödinger equations and applications
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Bound and ground states of coupled nonlinear Schrödinger equations
• Minimal energy solutions for cooperative nonlinear Schrödinger systems
• On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• Ground States and Bound States of a Nonlinear Schrödinger System
• Existence and uniqueness of positive solutions of nonlinear Schrödinger systems
• Standing waves of some coupled nonlinear Schrödinger equations