Existence results for nonlinear elliptic \overrightarrow{p}(\cdot)-equations

This paper investigates the existence of distributional solutions for a class of nonlinear elliptic \overrightarrow{p}(\cdot)-equations, the analysis focuses on the right-hand side, which comprises of a datum f\in L^{\overrightarrow{p'}(\cdot)}(\Omega) that is independent of u, and a compound nonlinear term involving a given function g \in L^{\overrightarrow{p}(\cdot)}(\Omega), the solution  u and its partial derivatives \partial_iu,\,i\in\{۱,\ldots,N\}, where L^{\overrightarrow{p}(\cdot)}(\Omega) and L^{\overrightarrow{p'}(\cdot)}(\Omega) represent the variable exponents anisotropic Lebesgue spaces.

کلیدواژه ها:

Variable exponent ، Nonlinear elliptic equation ، Anisotropic Lebesgue-Sobolev space ، Distributional solution ، existence ، Compound nonlinearity