Spectral analysis of eigenvalue problem with the (p(x),q(x))-Laplacian

Authors

  • Elson Musinguzi Department of Mathematics, Kampala International University, Uganda
  • Ibrahim Yale Faculty of Science and Technology, Kampala International University, Uganda
  • Mohammad Lubega Department of Science, Kampala International University, Uganda
  • Godiriva Atuhairwe Department of Science, Kampala International University, Uganda
  • Shafik Abdulhamidu Department of Science, Kampala International University, Uganda

DOI:

https://doi.org/10.56947/amcs.v25.389

Keywords:

Eigenvalues, Ljusternik-Schnirelmann principle, Spectral analysis

Abstract

In this study, a spectral problem that involves the Robin (a(x),b(x))-Laplacian on a bounded domain in Rn is analyzed. With the help of the  Ljusternik-Schnirelmann principle, it is established that an increasing sequence of eigenvalues exists.  Using the min-max principle, we also established that  the infimum of the spectrum is zero, and all the eigenvalues are non-negative. It was further proved that there exists a principal eigenvalue for this problem and that the spectrum is open.

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Published

2024-11-09

Issue

Section

Articles