Existence results for some nonlinear elliptic system with lack of compactness

DOI10.1016/S0362-546X(02)00151-7zbMath1087.35043OpenAlexW1965284225MaRDI QIDQ1863484

Jean Velin

Publication date: 11 March 2003

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/s0362-546x(02)00151-7

zbMATH Keywords

critical exponentelliptic systemlocal minimizationpseudo-Laplaciannon-compactness

Mathematics Subject Classification ID

Related Items (18)

Critical growth fractional elliptic systems with exponential nonlinearity ⋮ Existence result for variable exponents elliptic system with lack of compactness ⋮ The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent ⋮ Extremal regions and multiplicity of positive solutions for singular superlinear elliptic systems with indefinite-sign potential ⋮ Multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions ⋮ A CRITERION FOR EXISTENCE OF A POSITIVE SOLUTION OF A NONLINEAR ELLIPTIC SYSTEM ⋮ Existence of entire positive solutions for a critical system of nonlinear elliptic equations ⋮ Quasilinear elliptic system with coupling on nonhomogeneous critical term ⋮ The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions ⋮ An existence result for a class of \(p\)-Laplacian elliptic systems involving homogeneous nonlinearities in \(\mathbb R^N\) ⋮ The Nehari manifold for systems of nonlinear elliptic equations ⋮ On a nonhomogeneous elliptic system with changing sign data ⋮ Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in \(\mathbb R^N\) ⋮ A system of p-Laplacian equations on the Sierpiński gasket ⋮ Existence of nontrivial solutions for \(p\)-Laplacian variational inclusion systems in \(\mathbb R^N\) ⋮ Existence result for quasilinear elliptic problem on unbounded domains ⋮ Unnamed Item ⋮ Mountain pass solutions for the coupled systems of second and fourth order elliptic equations

Cites Work

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• The concentration-compactness principle in the calculus of variations. The limit case. I
• Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Résultats d'existence et de non-existence pour la solution positive et bornée d'une e.d.p. elliptique non linéaire
• Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations

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