Asia Mathematika
Published April 27, 2021 | Version v1
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Existence and nonexistence results for p-Laplacian Kirchhoff equation

Authors/Creators

  • 1. High School of Management and Abou Bekr Belkaid University, Tlemcen, Algeria
  • 2. Ecole Superieure de Management de Tlemcen and Laboratoire du controle des EDP Universite Djillali Liabes de Sidi Bellabes, Algeria
  • 3. Abou Bekr Belkaid University, Tlemcen, Algeria

Description

This paper is dedicated to investigating the following elliptic equation with Kirchhof type involving the p-Laplacian operator:

where \(\Omega\) is a bounded domain in \(\mathbb{R} ^{n}\left( n>3\right) , \ \Delta _{p}u:=-div\left( |\nabla u|^{p-2}\nabla u\right) ,\)  for 1<p<n denotes the p-Laplacian operator,
and \(\lambda >0\) is a real parameter and $a,b\geq 0:a+b>0$ are parameters. 

Using variational methods and critical points theory, we prove that the above problem has a positive solution and multiplicity results in certain cases. Our result is regarded as general which extends the results of related literature. At the end, we give some real applications.

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Journal article: 2457-0834 (ISSN)

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