Quasi-Lower C2 Functions and Their Application to Nonconvex Variational Problems

This study presents a novel category of nonconvex functions in Banach spaces, referred to as quasi-lower C2 functions on nonempty closed sets. We establish the existence of solutions for nonconvex variational problems involving quasi-lower C2 functions defined in Banach spaces. To illustrate the applicability of our findings, an example is provided in Lp spaces.