Electron. J. Differential Equations, Vol. 2019 (2019), No. 95, pp. 1-12.

Nonexistence results for weighted p-Laplace equations with singular nonlinearities

Kaushik Bal, Prashanta Garain

Abstract:
In this article we present some nonexistence results concerning stable solutions to the equation
$$ \hbox{div}\big(w(x)|\nabla u|^{p-2}\nabla u\big) =g(x)f(u)\quad \text{in }\mathbb{R}^N,\;p\geq 2 $$
when f(u) is either $u^{-\delta}+u^{-\gamma}$ with $\delta,\gamma>0$ or $e^{1/u}$ where w,g are suitable weight functions.

Submitted November 28, 2018. Published July 30, 2019.
Math Subject Classifications: 35A01, 35B93, 35J92.
Key Words: p-Laplacian; nonexistence; stable solution.

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Kaushik Bal
Department of Mathematics and Statistics
Indian Institute of Technology
Kanpur, UP-208016, India
email: kaushik@iitk.ac.in
Prashanta Garain
Department of Mathematics and Statistics
Indian Institute of Technology
Kanpur, UP-208016, India
email: pgarain@iitk.ac.in

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