Quasi-Lower <i>C</i>² Functions and Their Application to Nonconvex Variational Problems

Abstract

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.

Keywords

• quasi-lower <i>C</i>² functions
• nonvonvex variational problems
• nonvonvex variational inequalities
• generalized (<i>f</i>,<i>λ</i>)-projection
• <i>q</i>-uniformly convex Banach spaces
• uniformly <i>V</i>-prox-regular sets