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Volume 7, Number 3, 2017, Pages 1139-1160                                                                DOI:10.11948/2017071
On solvability of a class of nonlinear elliptic type equation with variable exponent
Ugur Sert and Kamal Soltanov
Keywords:PDEs with nonstandart nonlinearity, solvability theorem, variable exponent, implicit degenerate PDEs.
Abstract:
      In this paper, we study the Dirichlet problem for the implicit degenerate nonlinear elliptic equation with variable exponent in a bounded domain $\Omega \subset \mathbb{R}^{n}$. We obtain sufficient conditions for the existence of a solution without regularization and any restriction between the exponents. Furthermore, we define the domain of the operator generated by posed problem and investigate its some properties and also its relations with known spaces that enable us to prove existence theorem.
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