Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent

Abstract

We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer's fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.

Keywords

• variable exponent
• quasilinear equation
• schaeffer's fixed point
• subsolution
• supersolution
• weak solution