A linear perturbed Palais-Smale condition for lower semicontinuous functions on Banach spaces

Abstract

This paper introduces a notion of linear perturbed Palais-Smale condition for real-valued functions on Banach spaces. In terms of strongly exposed points, it presents a characterization which guarantees linear perturbed Palais-Smale condition holds for lower semicontinuous functions with bounded effective domains defined on a Banach space with the Radon-Nikodým property; and gives an example showing that linear perturbed P-S condition is strictly weaker than the P-S condition.