on homoclinic orbits for a class of noncoercive superquadratic hamiltonian systems

in this paper, we prove the existence of homoclinic solutions for a class of noncoercive first order hamiltonian systems j ˙x − m(t)x + u^∗g′(t, u(x)) = 0, by the minimax methods in critical point theory, specially, a generalized mountain pass theorem, when u is a linear operator with adjoint u∗ and g(t, y) satisfies the superquadratic condition g(t,x) /|y|² −→ −+∞as |y| −→ ∞, uniformly in t, and need not satisfy the global ambrosetti–rabinowitz condition.