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arXiv · 1804.03812

Existence of multiple solutions to an elliptic problem with measure data

Amita Soni·D. Choudhuri
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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 $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain with $N \geq 3$, $1 < q^{\prime} < q < p-1; \; \lambda,\;$ and $f$ satisfies certain conditions, $\mu>0$ is a Radon measure, $q^{\prime}=\frac{q}{q-1}$ is the conjugate of $q$.

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Amita Soni, D. Choudhuri. 2018-04-11. Existence of multiple solutions to an elliptic problem with measure data. https://arxiv.org/abs/1804.03812

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