Positive radial solutions of a nonlinear boundary value problem

Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla

Research output: Contribution to journalArticle

Abstract

© 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.
Original languageEnglish
Pages (from-to)1765-1783
Number of pages19
JournalCommunications on Pure and Applied Analysis
DOIs
Publication statusPublished - 1 Sep 2018

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