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Positivity

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Asymptotic behavior of ground state radial solutions for problems involving the \(\Phi \)-Laplacian

  • Abdelwaheb DhifliEmail author
  • Rym Chemmam
  • Syrine Masmoudi
Article
  • 28 Downloads

Abstract

We are concerned with the existence of positive solutions to the following boundary value problem in \((0,\infty ),\)
$$\begin{aligned} \frac{1}{A}\left( A\phi \left( \left| u^{\prime }\right| \right) u^{\prime }\right) ^{\prime }=-a(t)u^{\alpha },t>0,\left( A\phi \left( \left| u^{\prime }\right| \right) u^{\prime }\right) \left( 0\right) =0\text { and}\lim \nolimits _{t\rightarrow +\infty }u(t)=0, \end{aligned}$$
where \(\alpha \ge 0,\)\(\phi \) is a nonnegative continuously differentiable function on \(\left[ 0,\infty \right) \), A is a continuous function on \( \left[ 0,\infty \right) \), differentiable, positive on \(\left( 0,\infty \right) \) and a is a nonnegative function satisfying some appropriate assumptions related to Karamata regular variation theory. We give also, estimates on such solutions.

Keywords

Quasilinear elliptic equation \(\Phi \)-Laplacian operator Positive solutions Asymptotic behaviour 

Mathematics Subject Classification

34B18 35B40 31C15 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abdelwaheb Dhifli
    • 1
    Email author
  • Rym Chemmam
    • 2
  • Syrine Masmoudi
    • 2
  1. 1.Institut préparatoire aux etudes d’ingénieurs d’el Manar, LR10ES09 Modélisation mathématique, Analyse harmonique et théorie du potentielUniversité Tunis El ManarTunisTunisie
  2. 2.Faculté des sciences de Tunis, LR10ES09 Modélisation mathématique, Analyse harmonique et théorie du potentielUniversité Tunis El ManarTunisTunisie

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