On a singular elliptic problem with variable exponent

Abstract

"In the present note we study a semilinear elliptic Dirichlet problem involving a singular term with variable exponent of the following type $$\left\{ \begin{array}{ll} -\Delta u= \frac{f(x)}{u^{\gamma(x)} }, & \hbox{ in } \Omega \\ u>0, & \hbox{ in } \Omega \\ u=0, & \hbox{on } \partial \Omega \end{array} \right.\eqno{(\mathcal{P})}$$ Existence and uniqueness results are proved when $f\geq 0$."