English

Existence of multiple solutions to an elliptic problem with measure data

Analysis of PDEs 2018-04-12 v1

Abstract

In this paper we prove the existence of multiple nontrivial solutions of the following equation. \begin{align*} \begin{split} -\Delta_{p}u & = \lambda |u|^{q-2}u+f(x,u)+\mu\,\,\mbox{in}\,\,\Omega, u & = 0\,\, \mbox{on}\,\, \partial\Omega; \end{split} \end{align*} where ΩRN\Omega \subset \mathbb{R}^N is a smooth bounded domain with N3N \geq 3, 1<q<q<p1;  λ,  1 < q^{\prime} < q < p-1; \; \lambda,\; and ff satisfies certain conditions, μ>0\mu>0 is a Radon measure, q=qq1q^{\prime}=\frac{q}{q-1} is the conjugate of qq.

Keywords

Cite

@article{arxiv.1804.03812,
  title  = {Existence of multiple solutions to an elliptic problem with measure data},
  author = {Amita Soni and D. Choudhuri},
  journal= {arXiv preprint arXiv:1804.03812},
  year   = {2018}
}
R2 v1 2026-06-23T01:20:04.304Z