Positive solutions for a p-Laplacian equation arising from micro-electromechanical systems model

Abstract

In the present research paper, we investigate the positive solutions of the equation ΔpV=g(|x|)V−q(x),x∈RN, where N>p>2, 0<q≠1 and g is a continuous radial and strictly positive function on [0,+∞[.We consider various assumptions on the function g and delve into the intricate analysis of sky states and singular sky states solutions through logarithmic transformations. Additionally, we apply the theory of invariant manifolds in dynamical systems to establish the uniqueness of singular sky states.