Existence of extremal periodic solutions for quasilinear parabolic equations

Existence of extremal periodic solutions for quasilinear parabolic equations

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In this paper we consider a quasilinear parabolic equation in a bounded domain under periodic Equipment Dirichlet boundary conditions.Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower Inline - Roller Skates solutions.The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.