Differential and Integral Equations

Existence and multiplicity of solutions for nonlocal Neumann problem with non-standard growth

Francisco Julio S.A. Corrêa and Augusto César dos Reis Costa

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Abstract

In this paper, we are concerned with questions of existence of solution for a nonlocal and non-homogeneous Neumann boundary value problems involving the $p(x)$-Laplacian in which the non-linear terms have critical growth. The main tools we will use are the generalized Sobolev spaces and the Mountain Pass Theorem.

Article information

Source
Differential Integral Equations Volume 29, Number 3/4 (2016), 377-400.

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1455806029

Mathematical Reviews number (MathSciNet)
MR3466171

Zentralblatt MATH identifier
06562181

Subjects
Primary: 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Corrêa, Francisco Julio S.A.; Costa, Augusto César dos Reis. Existence and multiplicity of solutions for nonlocal Neumann problem with non-standard growth. Differential Integral Equations 29 (2016), no. 3/4, 377--400. https://projecteuclid.org/euclid.die/1455806029.


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