The critical case for a Berestycki-Lions theorem

DOI10.1007/s11425-013-4687-9zbMath1304.35241OpenAlexW2259889952MaRDI QIDQ476738

Jian Zhang, Wen Ming Zou

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-013-4687-9

zbMATH Keywords

Schrödinger equationground states solutions

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10)

Related Items (24)

Existence of ground state solutions for a class of quasilinear Schrödinger equations with general critical nonlinearity ⋮ Ground state solutions for critical Schrödinger equations with Hardy potential ⋮ Existence and asymptotic behavior of ground state solutions for Schrödinger equations with Hardy potential and Berestycki-Lions type conditions ⋮ Multiple entire solutions of fractional Laplacian Schrödinger equations ⋮ Global dynamics above the ground state energy for the combined power-type nonlinear Schrödinger equations with energy-critical growth at low frequencies ⋮ A remark on Kirchhoff-type equations in ℝ⁴ involving critical growth ⋮ Non-existence of ground states and gap of variational values for \(3D\) Sobolev critical nonlinear scalar field equations ⋮ Ground state solutions for Choquard equations with Hardy potentials and critical nonlinearity ⋮ Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension ⋮ Asymptotic property of ground states for a class of quasilinear Schrödinger equation with \(H^1\)-critical growth ⋮ Ground state solution for a class of Schrödinger equations involving general critical growth term ⋮ Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies ⋮ Choquard equations with critical nonlinearities ⋮ Existence of a ground state solution for Choquard equation with the upper critical exponent ⋮ Existence of a ground state and blowup problem for a class of nonlinear Schrödinger equations involving mass and energy critical exponents ⋮ Ground state solutions and multiple solutions for nonhomogeneous Schrödinger equations with Berestycki–Lions type conditions ⋮ Non-Nehari manifold method for asymptotically periodic Schrödinger equations ⋮ A study on the critical Kirchhoff problem in high-dimensional space ⋮ Existence of a ground state solution for Choquard equations involving critical Sobolev exponents ⋮ Some results on standing wave solutions for a class of quasilinear Schrödinger equations ⋮ A singular perturbed problem with critical Sobolev exponent ⋮ Ground state solution for critical Schrödinger equation with harmonic potential ⋮ Fractional Sobolev embedding with radial potential ⋮ Ground state solutions for a quasilinear elliptic equation with general critical nonlinearity

Cites Work

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• A BERESTYCKI–LIONS THEOREM REVISITED
• Homoclinic type solutions for a semilinear elliptic PDE on ℝⁿ
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
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• Existence and multiplicity results for some superlinear elliptic problems on R^N

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