Standing waves with a critical frequency for nonlinear Schrödinger equations involving critical growth

DOI10.1016/j.aml.2016.07.012zbMath1351.35199OpenAlexW2493640288MaRDI QIDQ311744

Jian Jun Zhang

Publication date: 13 September 2016

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2016.07.012

zbMATH Keywords

critical growthAmbrosetti open problemcritical frequencytruncation approach

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (4)

Existence and concentration results for the general Kirchhoff-type equations ⋮ The existence of the sign-changing solutions for the Kirchhoff-Schrödinger-Poisson system in bounded domains ⋮ A unified approach to singularly perturbed quasilinear Schrödinger equations ⋮ The existence result for a class of \(p\)-Kirchhoff-type problem with a multilinear growth nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials
• Nonlinear scalar field equations. I: Existence of a ground state
• Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials
• Multi-bump bound states of Schrödinger equations with a critical frequency
• Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger-Moser type
• Nonlinear Schrödinger equations with vanishing and decaying potentials.
• Bound states of nonlinear Schrödinger equations with potentials tending to zero at infinity
• Symmetry and monotonicity of least energy solutions
• On a class of nonlinear Schrödinger equations
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Singularly perturbed nonlinear Dirichlet problems involving critical growth
• Standing waves of nonlinear Schrödinger equations with optimal conditions for potential and nonlinearity
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• A BERESTYCKI–LIONS THEOREM REVISITED
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Multiscale-bump standing waves with a critical frequency for nonlinear Schrödinger equations
• Semi-Classical Bound States for Schrödinger Equations with Potentials Vanishing or Unbounded at Infinity
• A remark on least energy solutions in $\mathbf {R}^N$
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity

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