### Variational and penalization methods for studying connecting orbits of Hamiltonian systems.

Chen, Chao-Nien, Tzeng, Shyuh-yaur (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Chen, Chao-Nien, Tzeng, Shyuh-yaur (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Schechter, Martin (2006)

Boundary Value Problems [electronic only]

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Gregory S. Spradlin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.

Zhang, Peng, Tang, Chun-Lei (2010)

Abstract and Applied Analysis

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Cordaro, Giuseppe (2003)

Abstract and Applied Analysis

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Liang Zhang, X. H. Tang (2013)

Applications of Mathematics

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In this paper, we deal with the existence of periodic solutions of the $p\left(t\right)$-Laplacian Hamiltonian system $$\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}\left(\right|\dot{u}\left(t\right){|}^{p\left(t\right)-2}\dot{u}\left(t\right))=\nabla F(t,u\left(t\right))\phantom{\rule{1.0em}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in [0,T],\hfill \\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0.\hfill \end{array}\right.$$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.

Rabinowitz, Paul H. (1995)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Chen, Chao-Nien, Tzeng, Shyuh-yaur (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Boughariou, Morched (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Xingyong Zhang, Yinggao Zhou (2010)

Applications of Mathematics

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The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system $$\left\{\begin{array}{c}\ddot{u}\left(t\right)=\nabla F(t,u\left(t\right)),\phantom{\rule{5.0pt}{0ex}}\text{a.e.}\phantom{\rule{4pt}{0ex}}t\in [0,T],\hfill \\ u\left(0\right)-u\left(T\right)=\dot{u}\left(0\right)-\dot{u}\left(T\right)=0.\hfill \end{array}\right.$$ Some new existence theorems are obtained by the least action principle.