One Generalized Critical Point Theorem and its Applications on Super-quadratic Hamiltonian Systems

@article{Xing2016OneGC,
  title={One Generalized Critical Point Theorem and its Applications on Super-quadratic Hamiltonian Systems},
  author={Qin Xing and Fei Guo and Xiaofei Zhang},
  journal={Taiwanese Journal of Mathematics},
  year={2016},
  volume={20},
  pages={1093-1116}
}
In this paper, we prove a generalized critical point theorem under the condition (C), which is weaker than the (PS) condition. As its applications, we obtain the existence of the solutions for the Hamiltonian systems with a new super-quadratic conditions generalizing one in papers [2] and [12]. 
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References

SHOWING 1-10 OF 10 REFERENCES
The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous, periodic, and symmetric coefficients is established. This formula yields a new…
Periodic solutions of Hamiltonian systems with anisotropic growth
In this paper we obtain some existence and multiplicity results for periodic solutions of nonautonomous Hamiltonian systems $\dot z(t)=J\nabla H(z(t),t)$ whose Hamiltonian functions may have…
Periodic and subharmonic solutions for a class of non-autonomous Hamiltonian systems
Periodic solutions of hamiltonian systems
Abstract : The existence of periodic solutions of Hamiltonian systems of ordinary differential equations is proved in various settings. A case in which energy is prescribed is treated in Section 1.…
Existence of periodic solutions of a particular type of super-quadratic Hamiltonian systems☆
Periodic solutions to Hamiltonian inclusions
Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
Minimal period solutions of nonlinear Hamiltonian systems
Periodic-Solutions of "Superquadratic" Hamiltonian Systems
Solutions of minimal period for a class of convex Hamiltonian systems