Genericity and existence of a minimum for scalar integral functionals

Abstract

This paper is concerned with the existence of a minimum in a Sobolev space for the functional $$F_g (x): = \int_0^T {g(x(t)){\text{ }}dt + \int_0^T {h(x'(t)){\text{ }}dt,{\text{ }}x(0) = a,{\text{ }}x(T) = b,} }$$ wherea,b are real numbers,g is a continuous map, andh is lower semicontinuous, satisfying adequate growth conditions.