© 2018 American Institute of Mathematical Sciences. All rights reserved. In this work we study the following quasilinear elliptic equation: |x|a?u-udiv= 0(a(|x|) + g(u))?= |x|ßupin ? on ?? where a is a positive continuous function, g is a nonnegative and nondecreasing continuous function, ? = BR, is the ball of radius R > 0 centered at the origin in RN, N = 3 and, the constants a, ß ? R, ? ? (0, 1) and p > 1. We derive a new Liouville type result for a kind of”broken equation”. This result together with blow-up techniques, a priori estimates and a fixed-point result of Krasnosel’skii, allow us to ensure the existence of a positive radial solution. In this paper we also obtain a non–existence result, proven through a variation of the Pohozaev identity.
Cerda, P., Iturriaga, L., Lorca, S., & Ubilla, P. (2018). Positive radial solutions of a nonlinear boundary value problem. Communications on Pure and Applied Analysis, 1765-1783. https://doi.org/10.3934/cpaa.2018084