Weighted Sobolev spaces and ground state solutions for quasilinear elliptic problems with unbounded and decaying potentials

DOI10.1186/1687-2770-2013-189zbMath1294.35012OpenAlexW2146178931WikidataQ59300962 ScholiaQ59300962MaRDI QIDQ2251614

Guoqing Zhang

Publication date: 14 July 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2013-189

zbMATH Keywords

weighted Sobolev spacesquasilinear elliptic problemsunbounded and decaying potentials

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20)

Related Items (6)

Existence results for a class of quasilinear Schrödinger equations with singular or vanishing potentials ⋮ Compactness and existence results in weighted Sobolev spaces of radial functions. II: Existence ⋮ Existence, uniqueness and qualitative properties of positive solutions of quasilinear elliptic equations ⋮ Compactness and existence results for the \(p\)-Laplace equation ⋮ Compactness and existence results for quasilinear elliptic problems with singular or vanishing potentials ⋮ Radial quasilinear elliptic problems with singular or vanishing potentials

Cites Work

• Embedding theorems and existence results for nonlinear Schrödinger-Poisson systems with unbounded and vanishing potentials
• Ground state solution for quasilinear elliptic equation with critical growth in \(\mathbb R^N\)
• Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity
• On a class of nonlinear Schrödinger equations
• Existence of solitary waves in higher dimensions
• Hardy inequalities and some critical elliptic and parabolic problems
• Semi-classical states of nonlinear Schrödinger equations: a variational reduction method
• Weighted Sobolev embedding with unbounded and decaying radial potentials
• Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity
• An improved Hardy-Sobolev inequality and its application
• NONLINEAR SCHRÖDINGER EQUATIONS WITH UNBOUNDED AND DECAYING RADIAL POTENTIALS

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