Existence of solutions for subquadratic convex or $B$-concave operator equations and applications to second order Hamiltonian systems

Abstract

This paper investigates solutions for subquadratic convex or $B$-concave operator equations. First, some existence results are obtained by the index theory and the critical point theory. Then, some applications to second order Hamiltonian systems satisfying generalized periodic boundary value conditions and Sturm–Liouville boundary value conditions are pointed out. In particular, some well known theorems about periodic solutions for second order Hamiltonian systems are special cases of these results.

Keywords

• subquadratic
• operator equations
• index theory
• critical point
• second order hamiltonian systems