Electron. J. Diff. Equ., Vol. 2015 (2015), No. 219, pp. 1-10.

No-flux boundary problems involving p(x)-Laplacian-like operators

Eugenio Cabanillas Lapa, Victor Pardo Rivera, Jose Quique Broncano

Abstract:
In this article we obtain weak solutions for a class nonlinear elliptic problems for the p(x)-Laplacian-like operators under no-flux boundary conditions. Our result is obtained using a Fredholm-type result for a couple of nonlinear operators, and the theory of variable exponent Sobolev spaces.

Submitted May 18, 2015. Published August 21, 2015.
Math Subject Classifications: 35D05, 35J60, 35J70.
Key Words: p(x)-Laplacian; variable exponent Sobolev space; Fredholm alternative.

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Eugenio Cabanillas Lapa
Instituto de Investigación
Facultad de Ciencias Matemáticas
UNMSM, Lima, Perú
email: cleugenio@yahoo.com
Victor Pardo Rivera
Instituto de Investigación
Facultad de Ciencias Matemáticas
UNMSM, Lima, Perú
email: vpardor@gmail.com
Jose quique Broncano
Instituto de Investigación
Facultad de Ciencias Matemáticas
UNMSM, Lima, Perú
email: jquiqueb@unmsm.edu.pe

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