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

Charkaoui Abderrahim, Fahim Houda, Alaa Nour Eddine

Opuscula Mathematica

2021

Vol. 41, no. 1

25--53

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.