Nonlinear Schrödinger equations with potentials vanishing at infinity

DOI10.1016/j.crma.2006.04.011zbMath1099.35127OpenAlexW2066775064MaRDI QIDQ2499699

Jean Van Schaftingen, Denis Bonheure

Publication date: 14 August 2006

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2006.04.011

zbMATH Keywords

semiclassical limitground statesbound statestationary nonlinear Schrödinger equations

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Singular perturbations in context of PDEs (35B25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20)

Related Items (13)

Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials ⋮ Ground states for a class of quasilinear Schrödinger equations with vanishing potentials ⋮ Existence and concentration of bound states of a class of nonlinear Schrödinger equations in \(\mathbb{R}^2\) with potential tending to zero at infinity ⋮ Existence and concentration of positive solutions for a system of coupled saturable Schrödinger equations ⋮ Solutions to degenerative generalized quasilinear Schrödinger equations involving vanishing potentials and critical exponent ⋮ Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima ⋮ Asymptotically linear Schrödinger equation with potential vanishing at infinity ⋮ Bound state solutions for a class of nonlinear Schrödinger equations ⋮ Semi-classical states for the Choquard equation ⋮ Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials ⋮ Remarks on a class of nonlinear Schrödinger equations with potential vanishing at infinity ⋮ Existence and concentration of ground states of fractional nonlinear Schrödinger equations with potentials vanishing at infinity ⋮ Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field

Cites Work

• Bound state solutions for a class of nonlinear Schrödinger equations
• Semi-classical states for nonlinear Schrödinger equations
• Semiclassical states of nonlinear Schrödinger equations
• Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
• Multiplicity results for some nonlinear Schrödinger equations with potentials

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