Ground states of a system of nonlinear Schrödinger equations with periodic potentials

DOI10.1080/03605302.2016.1209520zbMath1353.35267arXiv1411.5582OpenAlexW3100689391MaRDI QIDQ2833302

Jarosław Mederski

Publication date: 17 November 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5582

zbMATH Keywords

variational methodsground statestrongly indefinite functionalBose-Einstein condensatesSchrödinger systemNehari-Pankov manifoldphotonic crystalsgap soliton

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Second-order elliptic systems (35J47) Soliton solutions (35C08)

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Cites Work

• Unnamed Item
• Unnamed Item
• An optimal constant for the existence of least energy solutions of a coupled Schrödinger system
• On superlinear Schrödinger equations with periodic potential
• A local mountain pass type result for a system of nonlinear Schrödinger equations
• Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials
• Positive solutions for a weakly coupled nonlinear Schrödinger system
• Periodic nonlinear Schrödinger equation with application to photonic crystals
• Radial solutions and phase separation in a system of two coupled Schrödinger equations
• Multipulse phases in k-mixtures of Bose-Einstein condensates
• Ground state solutions for some indefinite variational problems
• Minimum action solutions of some vector field equations
• Critical point theorems for indefinite functionals
• Segregated and synchronized vector solutions for nonlinear Schrödinger systems
• Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
• Bound and ground states of coupled nonlinear Schrödinger equations
• A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
• Least energy solitary waves for a system of nonlinear Schrödinger equations in \({\mathbb{R}^n}\)
• Semiclassical states for weakly coupled nonlinear Schrödinger systems
• Ground state of \(N\) coupled nonlinear Schrödinger equations in \(\mathbb R^n\), \(n \leq 3\)
• A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
• Schrödinger semigroups
• Deformation theorems on non-metrizable vector spaces and applications to critical point theory
• On decay of solutions to nonlinear Schrödinger equations
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• On a Schrodinger equation with periodic potential and spectrum point zero
• AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART
• Variational Methods

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