TY - JOUR
T1 - Critical Point Theorems of Non-Smooth Functionals Without the Palais-Smale Condition
AU - Boukhrisse , Hafida
AU - Allali , Zakaria El
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 303
EP - 317
PY - 2025
DA - 2025/02
SN - 7
DO - http://doi.org/10.12150/jnma.2025.303
UR - https://global-sci.org/intro/article_detail/jnma/23827.html
KW - Critical point, minimax theorems, locally Lipschitz functional,
the least action principle, perturbation argument.
AB - <p style="text-align: justify;">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 $\Phi$ : $E → R,$ 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.</p>