The paper deals with second order Hamiltonian systems of the form
where , is a symmetric positive definite matrix, and the function can change sign. The aim is to find non-trivial homoclinic orbits through 0. The author proves three theorems giving the conditions for existence of these orbits.
The existence of homoclinic orbits of such systems has been studied by many mathematicians, and the considered generalization concerns a new kind of “superquadratic” condition on and the assumption changing sign of function ; in so doing may be non-periodic.