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 is a semipositive symmetric continuous matrix and satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.

Keywords

L-index / Nontrivial solution / Hamiltonian systems / Lagrangian boundary conditions / Superquadratic condition

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