Abstract

We establish the existence of a $T$-$p(x)$-solution for the $p(x)$-elliptic problem $$ -{\rm div} (a(x,u,\nabla u))+g(x,u)=f-{\rm div} F\quad\mbox{ in } \varOmega, $$ where $\varOmega$ is a bounded open domain of $\mathbb{R}^{N}$, $N\geq 2$ and $a:\varOm

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