We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and L1 data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder’s topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.
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.
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