Benboubker, Mohamed Badr et al., Entropy and renormalized solutions for nonlinear elliptic problem involving variable exponent and measure data, Acta mathematica Sinica. English series (Print) , 31(1), 2015, pp. 151-169
We give an existence result of entropy and renormalized solutions for strongly nonlinear elliptic equations in the framework of Sobolev spaces with variable exponents of the type: .div(a(x,u,.u)+.(u))+g(x,u,.u)=., where the right-hand side belongs to L 1(.) + W .1,p.(x)(.), -div(a(x, u,.u)) is a Leray-Lions operator defined from W .1,p.(x)(.) into its dual and . . C 0(.,.N). The function g(x, u,.u) is a non linear lower order term with natural growth with respect to |.u| satisfying the sign condition, that is, g(x, u,.u)u . 0.