Radial solutions for a Gelfand type quasilinear elliptic problem with quadratic gradient terms

Abstract

In this paper, for a positive parameter λ, we study the existence of solutions of quasilinear elliptic problems whose model is    −∆u + µ(x) 1 + u |∇u| 2 = λ(1 + u) p in Ω u = 0 on ∂Ω, where 0 < m ≤ µ(x) ≤ M and p > 1. A particular emphasis will be placed on the existence of radial solution when the domain is the unit ball and µ(x) ≡ 1.