Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 60, pp. 1-21.

Title: Multiplicity of solutions to an elliptic problem with
       singularity and measure data

Authors: Sekhar Ghosh        (National Inst. of Technology Rourkela, India)
         Akasmika Panda      (National Inst. of Technology Rourkela, India)
         Debajyoti Choudhuri (National Inst. of Technology Rourkela, India)

Abstract:
 In this article, we prove the existence of multiple nontrivial solutions
 to the equation
 $$\displaylines{
 -\Delta_{p}u = \frac{\lambda}{u^{\gamma}}+g(u)+\mu\quad \text{in }\Omega,\cr
 u = 0\quad \text{on } \partial\Omega,\cr
 u>0 \quad \text{in }\Omega,
 }$$
 where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain with
 $N \geq 3$, $1 < p-1 < q$, $ \lambda>0$, $\gamma>0$, g satisfies
 certain conditions, $\mu\geq 0$ is a bounded Radon measure.

Submitted April 16, 2018. Published May 06, 2019.
Math Subject Classifications: 35J60, 35J75, 35R06.
Key Words: Elliptic PDEs; p-Laplacian; Radon measure.