## Taiwanese Journal of Mathematics

### THE EXISTENCE OF HETEROCLINIC ORBITS FOR A SECOND ORDER HAMILTONIAN SYSTEM

#### Abstract

In this paper, via variational methods and critical point theory, we study the existence of heteroclinic orbits for the following second order nonautonomous Hamiltonian system $$\ddot{u} - \triangledown{F(t,u)} = 0,$$ where $u \in R^{n}$ and $F \in C^{1}(R \times R^{n}, R)$, $F \geq 0$. $\mathcal{M} \subset R^{n}$ be set of isolated points and $\sharp{\mathcal{M}} \geq 2$. For each $\xi \in \mathcal{M}$, there exists a positive number $\rho_{0}$ such that if $y \in B_{\rho_{0}}(\xi)$, then $F(t,y) \geq F(t,\xi)$ for all $t \in R$, where $B_{\rho_{0}}(\xi) = \{y \in R^{n} \mid \mid y - \xi \mid \lt \rho_{0}\}$. Under some more assumptions on $F(t,x)$ and $\mathcal{M}$, we prove that each point in $\mathcal{M}$ is joined to another point in $\mathcal{M}$ by a solution of our system.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 2 (2013), 749-764.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499705963

Digital Object Identifier
doi:10.11650/tjm.17.2013.2352

Mathematical Reviews number (MathSciNet)
MR3044532

Zentralblatt MATH identifier
1279.37040

#### Citation

Huang, Wennian; Tang, Xianhua. THE EXISTENCE OF HETEROCLINIC ORBITS FOR A SECOND ORDER HAMILTONIAN SYSTEM. Taiwanese J. Math. 17 (2013), no. 2, 749--764. doi:10.11650/tjm.17.2013.2352. https://projecteuclid.org/euclid.twjm/1499705963

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