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

  • Boubker Azeroual
  • Abderrahim Zertiti
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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