Homoclinic orbits of nonperiodic superquadratic Hamiltonian system (Q395622)

For a first-order nonperiodic Hamiltonian system \(\dot z=\mathcal J H_z(t,z)\) with \(H(t,z)=\frac 12 L(t)z\cdot z+R(t,z)\), under a series assumptions on the nonlinearity including the weak superquadratic condition, the authors prove the existence of at least one homoclinic orbit, which is a ground state solution of the Hamiltonian system, in a variational setting and using the method of the generalized Nehari manifold.