Critical Point Theorems of Non-Smooth Functionals Without the Palais-Smale Condition
Year: 2025
Author: Hafida Boukhrisse, Zakaria El Allali
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 303–317
Abstract
This paper introduces some new variants of abstract critical point theorems that do not rely on any compactness condition of Palais Smale type. The focus is on locally Lipschitz continuous functional Φ : E→R, where E is a reflexive banach space. The theorems are established through the utilization of the least action principle, the perturbation argument, the reduction method, and the properties of sub-differential and generalized gradients in the sense of F.H. Clarke. These approaches have been instrumental in advancing the theory of critical points, providing a new perspective that eliminates the need for traditional compactness constraints. The implications of these results are far-reaching, with potential applications in optimization, control theory, and partial differential equations.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2025.303
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 303–317
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Critical point minimax theorems locally Lipschitz functional the least action principle perturbation argument.
Author Details
Hafida Boukhrisse Email
Zakaria El Allali Email