Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques

ABSTRACT

This article deals with a quasilinear elliptic equation with variable exponent under a homogenous Dirichlet boundary-value condition, where nonlinearity also depends on the gradient of the solution. By using an iterative method based on Mountain Pass techniques, the existence of a positive solution is obtained.

KEYWORDS:

• Iteration methods
• Mountain Pass theorem
• p(x)-Laplacian
• variable exponent Sobolev spaces

MATHEMATICS SUBJECT CLASSIFICATION:

• 35J35
• 35J60
• 35J70
• 35D30

Acknowledgement

The authors would like to express sincere thanks to the anonymous referee for carefully reading the manuscript and making valuable comments and suggestions.