Electron. J. Differential Equations, Vol. 2019 (2019), No. 60, pp. 1-21.

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

Sekhar Ghosh, Akasmika Panda, Debajyoti Choudhuri

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 6, 2019.
Math Subject Classifications: 35J60, 35J75, 35R06.
Key Words: Elliptic PDEs; p-Laplacian; Radon measure

Show me the PDF file (395 KB), TEX file for this article.

Sekhar Ghosh
Department of Mathematics
National Institute of Technology
Rourkela, India
email: sekharghosh1234@gmail.com
Akasmika Panda
Department of Mathematics
National Institute of Technology
Rourkela, India
email: akasmika44@gmail.com
Debajyoti Choudhuri
Department of Mathematics
National Institute of Technology
Rourkela, India
email: dc.iit12@gmail.com

Return to the EJDE web page