Stability Properties of Positive Solutions to a Quasilinear Elliptic Equation Involving the $p$-Laplacian and Indefinite Weight

Ghasem A. Afrouzi, Saleh Shakeri

Abstract

In this note, we discuss the stability and instability results of
positive solutions the following reaction -diffusion equation
\begin{equation}\label{1}
\left\{\begin{array}{ll} -\Delta_p
u=m(x)u^{p-1}-u^{\gamma-1}-ch(x) & \textrm{ in }\Omega,\\
Bu=0  & \textrm{ on }\partial \Omega