Browsing by Author "Gouasmia, Abdelhamid"

Now showing 1 - 4 of 4
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    Discrete Picone inequalities and some applications
    (Université d'Oum El Bouaghi, 2023) Ouennas, Oumaima; Bekhouche, Amel; Gouasmia, Abdelhamid
    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.
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    Fractional and non-homogeneous eigenvalue problems
    (University of Oum El Bouaghi, 2024) Guezainia, Houda; Gouasmia, Abdelhamid
    The main objective of this thesis is to study the existence , non-existence , and regularity of the weak solution of the fractional non-homogenous problem involving fractional and non-homogenous operateurs by using the mountain pass theorem . We divided this work into two chapters: In the first chapter, we begin by providing an overview of the functional analysis used in this work and define the fractional sobolev espaceWs,p(Ù) ,moreover, definemethod of mountain pass theorem . the second chapter study the existence,non-existence, and regularity of the weak solutions.
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    Positive solutions of fractional p-Laplace and singular systems
    (Université de Larbi Ben M'hidi- Oum El Bouaghi, 2022) Sahbi, Abed El Ghafour; Elbouche, Chouaib; Gouasmia, Abdelhamid
    The main objective of this thesis is to detail the results presented in the papers [1] and [14]. More precisely, we study singular systems involving nonlinear and non-local operators. First, we will show the non-existence of positive classical solutions. Next, Schauder's Fixed Point Theorem guaranteed the existence of a positive weak solutions pair in the suitable conical shell, and then H?lder regularity results. Finally, we prove the uniqueness by applying a well-known Krasnoselski?i's argument. We recall some results in the paper [1] there that are used in the above results.
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    Positive weak solution to nonlocal problems with singular nonlinearity
    (Université de Larbi Ben M’hidi-Oum El Bouaghi, 2021) Hamouda, Aimen; Gouasmia, Abdelhamid
    The main objective of this thesis is detail of qualitative properties in the paper [6] More precisely, we prove the existence and the uniqueness of the weak solution nonlocal quasilinear singular problem. In this paper, the authors proved the existence of weak solution by approximation method and Sobolev regularity estimates. On the other hand, we give a recent study in [1], where the authors study further the above nonlinear fractional singular problem in case the presence of singular weight.