Mediterranean Journal of Mathematics   2016 年

2016.08.16

This paper is concerned with the existence of solutions to the following singular elliptic boundary value problem involving (Formula presented.)-Laplace operator(Formula presented.)Here, (Formula presented.) is a bounded domain with smooth boundary, and (Formula presented.) is a positive (Formula presented.) function on (Formula presented.). A ???compatibility condition??? on the couple (Formula presented.) is given for the problem to have at least one solution. More precisely, it is shown that the problem admits at least one solution if and only if there exists a (Formula presented.) such that (Formula presented.). This generalizes a previous result obtained by Sun and Zhang (Calc Var Partial Differ Equ 49:909??“922, 2014) who considered the case (Formula presented.).