Periodic solutions of differential equations and nonconvex functionals in the calculus of variations

Abstract

We develop a duality theory for functional and we prove the existence of a minimizer ū of f^c , where f^c ,is described by the biconjugate of L(x, u,.). One of the consequences of the duality is the Euler-Lagrange inclusion, which ū must satisfy. We also formulate relations between critical points of f^c and the minimum of the functional of Clarke.

Keywords:

• Periodic solutions
• Calculus of variations
• The Euler-Lagrange equation
• Duality theory
• Variationals principles