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arXiv · 1712.07389

Non-existence results for the weighted $p$-Laplace equation with singular nonlinearities

Kaushik Bal·Prashanta Garain
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Abstract

In this paper we present some non existence results concerning the stable solutions to the equation $$\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u)=g(x)f(u)\;\;\mbox{in}\;\;\mathbb{R}^N;\;\;p\geq 2$$ when $f(u)$ is either $u^{-\delta}+u^{-\gamma}$, $\delta,\gamma>0$ or $\exp(\frac{1}{u})$ and for a suitable class of weight functions $w,g$.

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Kaushik Bal, Prashanta Garain. 2017-12-20. Non-existence results for the weighted $p$-Laplace equation with singular nonlinearities. https://arxiv.org/abs/1712.07389

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