Multiplicity of positive solutions for a semilinear \(p\)-Laplacian system with Sobolev critical exponent

DOI10.1016/j.na.2010.06.066zbMath1206.35098OpenAlexW2034818855MaRDI QIDQ622363

Ying Shen, Ji Hui Zhang

Publication date: 31 January 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.06.066

zbMATH Keywords

Sobolev critical exponentNehari manifoldsemilinear \(p\)-Laplacian system

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Second-order elliptic systems (35J47) Positive solutions to PDEs (35B09) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Boundary value problems for second-order elliptic systems (35J57)

Related Items

Existence and boundedness of solutions for systems of quasilinear elliptic equations, Multiple solutions for \(p\)-Laplacian systems with critical homogeneous nonlinearity, Multiplicity of positive solutions for semilinear elliptic systems, Multiple positive solutions for semilinear elliptic systems, Multiple solutions for a class of biharmonic elliptic systems with Sobolev critical exponent, Multiplicity of positive solutions for a second-order elliptic system of Kirchhoff type, Nontrivial solutions for a quasilinear elliptic system, Multiple solutions of a quasilinear elliptic system involving the nonlinear boundary conditions on exterior domain, Existence and multiplicity results for critical growth polyharmonic elliptic systems, Multiplicity result for a critical elliptic system with concave-convex nonlinearities, Multiplicity of solutions for a class of quasilinear Schrödinger systems in \(\mathbb R^N\), Multiple nontrivial solutions for critical growth quasilinear elliptic systems, Unnamed Item

Cites Work

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• Existence and multiplicity of positive solutions for semilinear elliptic systems with Sobolev critical exponents
• Multiple positive solutions for a critical quasilinear elliptic system with concave-convex nonlinearities
• The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function.
• A convex-concave problem with a nonlinear boundary condition.
• Minimax theorems
• On semilinear elliptic equations involving concave--convex nonlinearities and sign-changing weight function
• Multiple positive solutions for semilinear elliptic systems with nonlinear boundary condition
• A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function
• Multiplicity of solutions for resonant elliptic systems
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions for the p-Laplacian: application of the fibrering method