On the existence of nontrivial solutions of a system of nonlinear partial differential equations
| dc.contributor.author | Abada, Asma | |
| dc.contributor.author | Slimani, K | |
| dc.date.accessioned | 2024-03-21T09:16:50Z | |
| dc.date.available | 2024-03-21T09:16:50Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | The purpose of this work is to study some nonlinear fractional differential problems with boundary conditions in a bounded domain in order to generalize some results from the classical differential problems to the fractional case, which has a diversity of applications in various fields, manly physics, engineering, mathematical biology, signal processing, and image processing. In this study, under some suitable conditions on the nonlinearities, we apply the Leray-Schauder degree and the Schauder fixed point theorem to establish the existence of solutions; also, the Banach principle of contraction and the absurd reasoning are applied to prove the uniqueness of solutions. The first problem is a coupled semilinear fractional Laplacian system in a fractional Sobolev space, and the second problem is a semilinear equation involving the distributional Riesz fractional gradient in a Bessel potential space. The third problem is a nonlocal nonlinear equation related to the distributional Riesz fractional derivative in a Bessel-potential space. Finally, the fourth problem is a nonlinear problem involving left and right Riemann-Liouville fractional derivatives in a new fractional space of Sobolev type, the study of this problem is illustrated with an example to affirm the validity of methods used. | |
| dc.identifier.uri | http://dspace.univ-skikda.dz:4000/handle/123456789/494 | |
| dc.language.iso | en | |
| dc.publisher | University 20 august 1955-Skikda | |
| dc.title | On the existence of nontrivial solutions of a system of nonlinear partial differential equations | |
| dc.type | Thesis |