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

Ayazoglu (Mashiyev) R., Ekincioglu İ.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.37, no.9, pp.1144-1157, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 9
  • Publication Date: 2016
  • Doi Number: 10.1080/01630563.2016.1205088
  • Title of Journal : NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Page Numbers: pp.1144-1157
  • Keywords: Iteration methods, Mountain Pass theorem, p(x)-Laplacian, variable exponent Sobolev spaces, ELLIPTIC-EQUATIONS, POSITIVE SOLUTIONS, MULTIPLE SOLUTIONS, EXISTENCE

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.