Weighted Sobolev type embeddings and coercive quasilinear elliptic equations on $\mathbb{R}^{N}$

DOI10.1090/S0002-9939-2011-11289-9zbMath1238.35034MaRDI QIDQ2880649

Jiabao Su, Rushun Tian

Publication date: 13 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

quasilinear elliptic equationSobolev type embeddingsub-\(p\)-linear nonlinearity

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (15)

Nonlinear Schrödinger equations without compatibility conditions on the potentials ⋮ Existence results for a class of quasilinear Schrödinger equations with singular or vanishing potentials ⋮ Schrödinger-Poisson systems with radial potentials and discontinuous quasilinear nonlinearity ⋮ Compactness and existence results in weighted Sobolev spaces of radial functions. II: Existence ⋮ Lions-type properties for the \(p\)-Laplacian and applications to quasilinear elliptic equations ⋮ Existence and multiplicity of solutions for Kirchhoff-type equation with radial potentials in \(\mathbb{R}^{3}\) ⋮ Sobolev type embeddings and an inhomogeneous quasilinear elliptic equation on \(\mathbb R^N\) with singular weights ⋮ Multiple solutions to elliptic equations on \(\mathbb{R}^N\) with combined nonlinearities ⋮ Quasilinear elliptic equations on \({\mathbb{R}}^{N}\) with singular potentials and bounded nonlinearity ⋮ Compactness and existence results in weighted Sobolev spaces of radial functions. I: Compactness ⋮ Ground state solutions for Schrödinger-Poisson systems with multiple weighted critical exponents ⋮ Radial nonlinear elliptic problems with singular or vanishing potentials ⋮ 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

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• Schrödinger equations with concave and convex nonlinearities
• NONLINEAR SCHRÖDINGER EQUATIONS WITH UNBOUNDED AND DECAYING RADIAL POTENTIALS
• NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Nonlinear boundary value problems with concave nonlinearities near the origin

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