Local super-quadratic conditions on homoclinic solutions for a second-order Hamiltonian system (Q1680768)

The author considers the following periodic Hamiltonian systems \[ \ddot{u}(t)-L(t)u+\nabla W(t,u)=0,\;\;t\in\mathbb{R}, \] where \(L(t)\) is \(T\)-periodic and \(W(t,u)\) is \(T\)-periodic with respect to \(t\). The author introduces a new superquadratic condition. Under this condition the author shows the existence of homoclinic solutions. Moreover, the author shows the novelty of his results on the basis of some known examples.