HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM

Abstract

In this paper, we study the following first-order nonperiodic Hamiltonian system $$\dot{z} = \mathcal {J}H_{z}(t,z),$$ where $H \in C^{1}(\mathbb{R} \times \mathbb{R}^{2N}, \mathbb{R})$ is the form $H(t,z) = \frac{1}{2} L(t)z \cdot z + R(t,z)$. Under weak superquadratic condition on the nonlinearitiy. By applying the generalized Nehari manifold method developed recently by Szulkin and Weth, we prove the existence of homoclinic orbits, which are ground state solutions for above system.