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 is a smooth bounded domain with , and satisfies certain conditions, is a Radon measure, is the conjugate of .
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}
}