Critical Point Theorems of Non-Smooth Functionals Without the Palais-Smale Condition (Journal of Nonlinear Modeling and Analysis, 2025)
This paper introduces some new variants of abstract critical pointtheorems 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 areflexive banach space. The theorems are established through the utilization ofthe least action principle, the perturbation argument, the reduction method,and the properties of sub-differential and generalized gradients in the senseof F.H. Clarke. These approaches have been instrumental in advancing thetheory of critical points, providing a new perspective that eliminates the needfor traditional compactness constraints. The implications of these results arefar-reaching, with potential applications in optimization, control theory, andpartial differential equations.