No--flux boundary value problems with anisotropic variable exponents

Maria-Magdalena Boureanu; Cristian Udrea

doi:10.3934/cpaa.2015.14.881

Article Contents

2015, Volume 14, Issue 3: 881-896. Doi: 10.3934/cpaa.2015.14.881

This issue Previous Article Admissibility, a general type of Lipschitz shadowing and structural stability Next Article Gradient estimates and comparison principle for some nonlinear elliptic equations

No--flux boundary value problems with anisotropic variable exponents

Maria-Magdalena Boureanu^1, and
Cristian Udrea^2,

1.
Department of Mathematics, University of Craiova, A.I. Cuza Street 13, 200585 Craiova
2.
Department of Applied Mathematics, University of Craiova, A.I. Cuza Street 13, 200585 Craiova

Received: May 31, 2014

Revised: October 31, 2014

Published: April 2015

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Abstract

We are concerned with elliptic problems involving generalized anisotropic operators with variable exponents and a nonlinearity $f$. For such problems with no-flux boundary conditions we establish the existence, the uniqueness, or the multiplicity of weak solutions, under various hypotheses.

Keywords:

Mathematics Subject Classification: Primary: 35J25, 35D30, 35J20; Secondary: 46E35.

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