## Abstract and Applied Analysis

### Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems

#### Abstract

We study the following nonperiodic Hamiltonian system $\stackrel{\dot{}}{z}=\mathcal{J}{H}_{z}(t,z)$, where $H\in {C}^{1}(\mathbb{R}{\times}{\mathbb{R}}^{2N},\mathbb{R})$ is the form $H(t,z)=(1/2)B(t)z\cdot z+R(t,z)$. We introduce a new assumption on $B(t)$ and prove that the corresponding Hamiltonian operator has only point spectrum. Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of homoclinic orbits for asymptotically quadratic nonlinearity as well as the existence of infinitely many homoclinic orbits for superquadratic nonlinearity.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 769232, 20 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495680

Digital Object Identifier
doi:10.1155/2012/769232

Mathematical Reviews number (MathSciNet)
MR2903829

Zentralblatt MATH identifier
1244.34070

#### Citation

Qin, Wenping; Zhang, Jian; Zhao, Fukun. Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems. Abstr. Appl. Anal. 2012 (2012), Article ID 769232, 20 pages. doi:10.1155/2012/769232. https://projecteuclid.org/euclid.aaa/1355495680

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