Three positive solutions for Dirichlet problems involving critical Sobolev exponent and sign-changing weight

DOI10.1016/j.jde.2010.07.021zbMath1200.35138OpenAlexW1965054503MaRDI QIDQ1958437

Tsung-fang Wu

Publication date: 29 September 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.07.021

zbMATH Keywords

critical Sobolev exponentsign-changing weightconcave-convex nonlinearitiesLusternik-Schnirelman categoryfibering map

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items (22)

Existence of multiple solutions for a quasilinear Neumann problem with critical exponent ⋮ Multiple positive solutions for a quasilinear elliptic system with critical exponent and sign-changing weight ⋮ Multiplicity of positive solutions for a class of concave-convex elliptic equations with critical growth ⋮ The Nehari manifold for a fractional critical Choquard equation involving sign-changing weight functions ⋮ Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions ⋮ Existence and multiplicity of positive solutions for a class of elliptic equations involving critical Sobolev exponents ⋮ Multiplicity and concentration of positive solutions for semilinear elliptic equations with steep potential ⋮ Estimates for extremal values for a critical fractional equation with concave-convex nonlinearities ⋮ The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent ⋮ On nonlocal Choquard system with Hardy-Littlewood-Sobolev critical exponents ⋮ Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent ⋮ The Nehari manifold for elliptic equation involving the square root of the Laplacian ⋮ Two solutions for an elliptic equation with fast increasing weight and concave-convex nonlinearities ⋮ The Choquard equation with weighted terms and Sobolev-Hardy exponent ⋮ Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains ⋮ Positive solution for an indefinite fourth-order nonlocal problem ⋮ On the semilinear fractional elliptic equations with singular weight functions ⋮ The Nehari Manifold for a p-Laplacian equation with concave-convex nonlinearities and sign-changing potential ⋮ Unnamed Item ⋮ Two solutions for a fourth order nonlocal problem with indefinite potentials ⋮ Multiple positive solutions for the critical Kirchhoff type problems involving sign-changing weight functions ⋮ Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains

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