English

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

Analysis of PDEs 2021-08-26 v2

Abstract

In this paper, we prove the existence of multiple nontrivial solutions of the following equation. \begin{align*} \begin{split} -\Delta_{p}u & = \frac{\lambda}{u^{\gamma}}+g(u)+\mu~\mbox{in}\,\,\Omega, u & = 0\,\, \mbox{on}\,\, \partial\Omega, u&>0 \,\,\mbox{in}\,\,\Omega, \end{split} \end{align*} where ΩRN\Omega \subset \mathbb{R}^N is a smooth bounded domain with N3N \geq 3, 1<p1<q1 < p-1 < q , λ>0 \lambda>0, γ>0\gamma>0, gg satisfies certain conditions, μ0\mu\geq 0 is a bounded Radon measure.

Keywords

Cite

@article{arxiv.1804.05590,
  title  = {Multiplicity of solutions to an elliptic problem with singularity and measure data},
  author = {S. Ghosh and A. Panda and D. Choudhuri},
  journal= {arXiv preprint arXiv:1804.05590},
  year   = {2021}
}

Comments

24 Pages