Variable exponents anisotropic nonlinear elliptic systems with L p ′ → ( ⋅ ) -data

Abstract

Our paper is devoted to studying the existence results of distributional solutions in the anisotropic Sobolev space with variable exponents and zero boundary W ˚ 1 , p → ( ⋅ ) ( Ω , R m ) for a family of boundary value problems, which is a variable exponent anisotropic nonlinear elliptic system with L p ′ → ( ⋅ ) data for the datum f (i.e. ∈ L p ′ → ( ⋅ ) ( Ω , R m ) ), and has a sum of two Carathéodory nonlinearities, one of which includes the solution u and the other its partial derivatives ∂ i u , i = 1 , … , N .