Some new critical point theorems and application
| dc.contributor.author | Djouadi, Lamis | |
| dc.contributor.author | MOKHTARI, Abdelhak: Supervisor. | |
| dc.date.accessioned | 2024-07-04T13:00:01Z | |
| dc.date.available | 2024-07-04T13:00:01Z | |
| dc.date.issued | 2024-06-11 | |
| dc.description.abstract | In this memory, we have studied new theorems : First, we proved the critical point theorem without satisfying the Palais-Smale condition, ensuring the existence of a critical point. Then, we demonstrated the existence of a critical point in Riesz-Banach space ordered by a cone k, followed by applying the abstract result to the following problem : ( −(p(t)u 0 (t))0 = f(t, u(t)), a.e.t ∈ [0, +∞) u(0) = u(+∞) = 0, (3) Where f : [0, +∞)R → R is a Caratheodory function, and may change sign, p : [0, +∞) → (0, +∞) satisfies 1 p ∈ L 1 [0, +∞), and Z +∞ 0 Z +∞ t 1 p(s) ds dt < +∞. In the second case, we established new theorems of fixed points in Hilbert spaces for potential α−positively homogeneous operators using the weak Ekeland principle, then applied our abstract result to the following problem : ( −u 00(t) = q(t)f(u(t))), t ∈ (0, 1), u(0) = u(1) = 0, (4) Where f : R → R is a continuous function, q ∈ L 2 (0, 1). | |
| dc.identifier.uri | https://dspace.univ-msila.dz/handle/123456789/43277 | |
| dc.language.iso | en | |
| dc.publisher | Mohamed Boudiaf University of M’sila, Faculty of Mathematics and Informatics, Department of Mathematics | |
| dc.subject | Critical point | |
| dc.subject | Fixed point | |
| dc.subject | Ekeland principle | |
| dc.subject | Weak solution | |
| dc.subject | Boundary problem | |
| dc.title | Some new critical point theorems and application | |
| dc.type | Thesis |