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arXiv · 1709.05400

Multiplicity results for a quasilinear equation with singular nonlinearity

Kaushik Bal·Prashanta Garain
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Abstract

For an open, bounded domain $\Om$ in $\mathbb{R}^N$ which is strictly convex with $C^2$ boundary, we show that there exists a $\land>0$ such that the singular quasilinear problem \begin{eqnarray*} &-\delp u =\cfrac{\lambda}{u^{\del}}+u^q\,\,\mbox{in}\,\,\Om\\ &u=0\,\,\mbox{on}\,\,\partial\Om;\, \,\,u>0\,\,\mbox{in}\,\,\Om \end{eqnarray*} admits atleast two solution $ u$ and $v$ in $W^{1,p}_{loc}(\Om)\cap L^{\infty}(\Om)$ for any $\del>0$ and $0<\lam<\land$ provided $1 0$.

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Kaushik Bal, Prashanta Garain. 2017-09-15. Multiplicity results for a quasilinear equation with singular nonlinearity. https://arxiv.org/abs/1709.05400

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