Multiplicity of positive solutions for a critical quasilinear elliptic system with concave and convex nonlinearities

DOI10.1016/J.JMAA.2012.05.078zbMath1255.35119OpenAlexW2028869609MaRDI QIDQ451016

Si. Mohammed Sbaï, Rachid Echarghaoui, Samira Benmouloud

Publication date: 26 September 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.05.078

zbMATH Keywords

quasilinear elliptic systemdeformationhomotopymultiple positive solutionsSobolev critical exponents\(p\)-Laplacian systemcontractible sets

Mathematics Subject Classification ID

Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92) Higher-order elliptic systems (35J48)

Related Items (12)

The numbers of positive solutions by the Lusternik-Schnirelmann category for a quasilinear elliptic system critical with Hardy terms ⋮ Multiple positive solutions for a fractional elliptic system with critical nonlinearities ⋮ Multiple positive solutions for a fractional \(p \& q\)-Laplacian system with concave and critical nonlinearities ⋮ A multiplicity results to a p-q Laplacian system with a concave and singular nonlinearities ⋮ Multiple positive solutions for a fractional Laplacian system with critical nonlinearities ⋮ Multiplicity of positive solutions for a \(p\)-\(q\)-Laplacian system with concave and critical nonlinearities ⋮ Multiple symmetric results for quasilinear elliptic systems involving singular potentials and critical Sobolev exponents in \(\mathbb{R}^N\) ⋮ Multiple positive solutions for semi-linear elliptic systems with sign-changing weight ⋮ Multiple positive solutions for a Choquard equation involving both concave-convex and Hardy-Littlewood-Sobolev critical exponent ⋮ Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities ⋮ Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight ⋮ Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent

Cites Work

• Variational methods in geometry
• Multiple positive solutions for \(p\)-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• Multiple positive solutions for a critical quasilinear elliptic system
• Multiple positive solutions for a critical quasilinear elliptic system with concave-convex nonlinearities
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• On systems of elliptic equations involving subcritical or critical Sobolev exponents
• Multiplicity of positive solutions to a \(p\)-Laplacian equation involving critical nonlinearity.
• Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents
• Minimax theorems
• A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function
• A multiplicity result for a variational problem with lack of compactness

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