The Nehari manifold for systems of nonlinear elliptic equations

DOI10.1016/j.na.2005.06.003zbMath1194.35132OpenAlexW2033124014MaRDI QIDQ2489500

Abdallah El Hamidi, Khalid Adriouch

Publication date: 28 April 2006

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.2005.06.003

zbMATH Keywords

Ekeland's principleNehari manifold\((p,q)\)-LaplacianPalais-Smale sequences

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Second-order elliptic systems (35J47) Quasilinear elliptic equations with (p)-Laplacian (35J92) Boundary value problems for second-order elliptic systems (35J57)

Related Items (37)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical point theory and Hamiltonian systems
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Combined effects of concave and convex nonlinearities in some elliptic problems
• The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function.
• On systems of elliptic equations involving subcritical or critical Sobolev exponents
• Nonvariational elliptic systems
• Existence results to elliptic systems with nonstandard growth conditions
• Multiple solutions with changing sign energy to a nonlinear elliptic equation
• On the variational principle
• Existence results for some nonlinear elliptic system with lack of compactness
• Existence of multiple solutions for quasilinear systems via fibering method
• Semilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions.
• Minimax theorems
• An eigenvalue problem for elliptic systems
• On a Class of Nonlinear Second-Order Differential Equations
• Positive splutions of semilinear elliptic systems
• On Superquadratic Elliptic Systems
• Positive solutions for the p-Laplacian: application of the fibrering method
• Nonlinear elliptic systems
• Positive radial solutions of nonlinear elliptic systems

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