ON SOLVABILITY OF A CLASS OF NONLINEAR ELLIPTIC TYPE EQUATIONS WITH VARIABLE EXPONENT

What is it about?

In this paper, we study the Dirichlet problem for the implicit degenerate nonlinear elliptic equation with variable exponent in a bounded domain Rn. We obtain sufficient conditions for the existence of a solution without regularization and any restriction between the exponents. Furthermore, we dene the domain of the operator generated by the posed problem and investigate its properties and its relations with known spaces that enable us to prove the existence theorem.

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Why is it important?

We obtain sufficient conditions for the existence of a solution without regularization and any restriction between the exponents. Furthermore, we dene the domain of the operator generated by the posed problem and investigate its properties and its relations with known spaces that enable us to prove the existence theorem