Existence of Sign Changing Radial Solutions for Elliptic Equation Involving the p-Laplacian on Exterior Domains

Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 37)

Abstract

In this paper we prove the existence of radial solutions having a prescribed number of sign change to the p-Laplacian \(\varDelta _{p} u+ f(u)= 0 \) on exterior domain of the ball of radius \( R > 0 \) centred at the origin in \(\mathbb {R}^{N}\). The nonlinearity f is odd and behaves like \( |u|^{q-1}u \) when u is large with \(1<p<q+1 \) and \( f<0\) on \((0,\beta )\), \( f>0 \) on \( (\beta ,\infty ) \) where \( \beta >0 \). The method is based on a shooting approach, together with a scaling argument.

Keywords

Exterior domain p-Laplacian Sign changing radial solution 

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Faculty of ScienceAbedelmalek Esaadi UniversityTetouanMorocco
  2. 2.Laboratoire d’Analyse Fonctionnel non Linèaire Application à la physique thèorique et la thèorie de la dynamique des populationsUniversité Abedelmalek EssaadiTetouanMorocco

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