TY - JOUR
T1 - Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
TT -
JF - IJMSI
JO - IJMSI
VL - 14
IS - 1
UR - http://ijmsi.ir/article-1-936-en.html
Y1 - 2019
SP - 95
EP - 119
KW - Elliptic equation
KW - Orlicz-Sobolev spaces
KW - Renormalized solution.
N2 - The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega, $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined from $W^{1}_{0}L_{M}(Omega)$ into its dual, $Phi in C^{0}(mathbb{R},mathbb{R}^{N})$. The function $g(x,u,nabla u)$ is a non linear lower order term with natural growth with respect to $|nabla u|$, satisfying the sign condition and the datum $mu$ is assumed belong to $L^1(Omega)+W^{-1}E_{overline{M}}(Omega)$.
M3
ER -