Existence and non-existence of solutions for a singular problem with variable potentials

Abstract

The purpose of this article is to prove some existence and nonexistence theorems for the inhomogeneous singular Dirichlet problem $$ - \Delta_p u = \frac{\lambda k(x)}{u^\delta}\pm h(x) u^q. $$ For proving our results we use the sub and super solution method, and monotonicity arguments.

Keywords

• Singular elliptic equation
• variational methods
• existence
• non-existence