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

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Innovations in Smart Cities and Applications (SCAMS 2017)

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

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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.

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Authors and Affiliations

  1. Faculty of Science, Abedelmalek Esaadi University, BP 2121, 93000, Tetouan, Morocco

    Boubker Azeroual

  2. Laboratoire d’Analyse Fonctionnel non Linèaire Application à la physique thèorique et la thèorie de la dynamique des populations, Université Abedelmalek Essaadi, BP 2121, 93000, Tetouan, Morocco

    Abderrahim Zertiti

Authors
  1. Boubker Azeroual
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  2. Abderrahim Zertiti
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Corresponding author

Correspondence to Boubker Azeroual .

Editor information

Editors and Affiliations

  1. Computer Sciences Department, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco

    Mohamed Ben Ahmed

  2. Computer Sciences Department, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco

    Anouar Abdelhakim Boudhir

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Azeroual, B., Zertiti, A. (2018). Existence of Sign Changing Radial Solutions for Elliptic Equation Involving the p-Laplacian on Exterior Domains. In: Ben Ahmed, M., Boudhir, A. (eds) Innovations in Smart Cities and Applications. SCAMS 2017. Lecture Notes in Networks and Systems, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-74500-8_84

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  • DOI: https://doi.org/10.1007/978-3-319-74500-8_84

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74499-5

  • Online ISBN: 978-3-319-74500-8

  • eBook Packages: EngineeringEngineering (R0)

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