A Priori Estimates for a Quasilinear Elliptic PDE

Abstract:

      In the recent past many results have been established on positive solutions to boundary value problems of the form - div (|Du(x)|^p-2Du(x))=λf(u(x))} in} Ω, u(x)=0 on (?)Ω,where λ>0, Ω is a bounded smooth domain and f(s)≥ 0 for s≥ 0 . In this paper we study a priori estimates of positive radial solutions of such problems when N>p>1, Ω=B₁={x∈R^N; | x |<1} and f∈C¹(0,∞)∩ C⁰([0,∞)), f(0)=0 .