Nontrivial solutions of superquadratic Hamiltonian systems with Lagrangian boundary conditions and the L-index theory

Abstract

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems \( \dot z \)(t) = J▽H(t, z(t)) with Lagrangian boundary conditions, where Open image in new window is a semipositive symmetric continuous matrix and Open image in new window satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.