A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH

DOI10.1017/S001708951300027XzbMath1296.35054MaRDI QIDQ5415955

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

Publication date: 19 May 2014

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

variational methods\(p(x)\)-Laplacianbi-nonlocal elliptic equation

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for higher-order elliptic equations (35J35)

Related Items (6)

Bi-nonlocal sixth order \(p(x)\)-problem with indefinite weight ⋮ Nonlocal Neumann problem with critical exponent from the point of view of the trace ⋮ Existence and multiplicity of solutions involving the \(p(x)\)-Laplacian equations: on the effect of two nonlocal terms ⋮ \(p(x)\)-Kirchhoff bi-nonlocal elliptic problem driven by both \(p(x)\)-Laplacian and \(p(x)\)-Biharmonic operators ⋮ An elliptic equation under the effect of two nonlocal terms ⋮ On a bi-nonlocal fourth order elliptic problem

Cites Work

• Nontrivial solutions of Kirchhoff-type problems via the Yang index
• Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
• Shear bands as surfaces of discontinuity
• Electrorheological fluids: modeling and mathematical theory
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Positive solutions for a quasilinear elliptic equation of Kirchhoff type
• A strong maximum principle for differential equations with nonstandard \(p(x)\)-growth conditions
• On an elliptic equation of p-Kirchhoff type via variational methods
• STATIONARY STATES IN PLASMA PHYSICS: MAXWELLIAN SOLUTIONS OF THE VLASOV-POISSON SYSTEM
• On a nonlocal elliptic equation with decreasing nonlinearity arising in plasma physics and heat conduction
• On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent
• On a variational approach to some non-local boundary value problems
• 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 \(W^{m,p(x)}(\Omega)\)

This page was built for publication: A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH