Nonlocal Neumann problem with critical exponent from the point of view of the trace

DOI10.1007/BF03377407zbMath1378.35117MaRDI QIDQ1691850

Augusto César dos Reis Costa, Francisco Julio Sobreira de Araujo Correa

Publication date: 25 January 2018

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

zbMATH Keywords

tracecritical exponentNeumann boundary conditionsgenusnonlocal problemSobolev spaces with variable exponent

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

Related Items

Multiplicity of solutions for a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents

Cites Work

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• Existence and multiplicity of solutions for nonlocal \(p(x)\)-Laplacian equations with nonlinear Neumann boundary conditions
• On the Sobolev trace theorem for variable exponent spaces in the critical range
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Infinitely many small solutions for the \( p (x)\)-Laplacian operator with nonlinear boundary conditions
• Existence and multiplicity of nontrivial solutions for a bi-nonlocal equation
• Dual variational methods in critical point theory and applications
• On nonlocal \(p(x)\)-Laplacian Dirichlet problems
• Boundary trace embedding theorems for variable exponent Sobolev spaces
• Solutions for Neumann boundary value problems involving \(p(x)\)-Laplace operators
• The concentration-compactness principle for variable exponent spaces and applications
• On a p(x)-Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument
• Existence of solution to a critical trace equation with variable exponent
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• On an elliptic equation of p-Kirchhoff type via variational methods
• A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)