Infinitely many homoclinic orbits for a class of superquadratic Hamiltonian systems

Abstract

In this paper, we prove the existence of infinitely many homoclinic orbits for the first order Hamiltonian systems $J\dot{x}-M(t)x+R^{\prime }(t,x)=0$, by the minimax methods in critical point theory, when $R(t,y)$ satisfies the superquadratic condition $\frac{R(t,x)}{\Vert x{\mathring{|}}^2}⟶\pm \infty$ as $\Vert x\Vert ⟶\infty$, uniformly in $t$, and need not satisfy the global Ambrosetti-Rabinowitz condition

13 pages