Discrete Picone inequalities and some applications
No Thumbnail Available
Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Université d'Oum El Bouaghi
Abstract
The main objective of this thesis is to study some problems related to eigenvalues and singular
ones. We employ variational methods in order to show the existence of positive weak solutions
in both cases. Thanks to the results obtained recently research together with a new version of
the Picone inequality, we also establish the uniqueness results.
We divided this work into three chapters:
In the first chapter, we begin by recalling some of the basic and preliminary concepts used in
this work.
The second chapter deals with the definition of Picone inequality in local and non-local cases,
which we will need in the next chapter.
The third chapter deals with the presence of existence, non-existence, regularity, and the
uniqueness of the weak solution to two problems related to non-local and non-homogeneous
operators, the first for the generalized eigenvalues and the second for the singular.