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2013 HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM
Jian Zhang, Xianhua Tang, Wen Zhang
Taiwanese J. Math. 17(6): 1855-1867 (2013). DOI: 10.11650/tjm.17.2013.3139

Abstract

In this paper, we study the following first-order nonperiodic Hamiltonian system $$\dot{z} = \mathcal {J}H_{z}(t,z),$$ where $H \in C^{1}(\mathbb{R} \times \mathbb{R}^{2N}, \mathbb{R})$ is the form $H(t,z) = \frac{1}{2} L(t)z \cdot z + R(t,z)$. Under weak superquadratic condition on the nonlinearitiy. By applying the generalized Nehari manifold method developed recently by Szulkin and Weth, we prove the existence of homoclinic orbits, which are ground state solutions for above system.

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Jian Zhang. Xianhua Tang. Wen Zhang. "HOMOCLINIC ORBITS OF NONPERIODIC SUPERQUADRATIC HAMILTONIAN SYSTEM." Taiwanese J. Math. 17 (6) 1855 - 1867, 2013. https://doi.org/10.11650/tjm.17.2013.3139

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1321.37065
MathSciNet: MR3141863
Digital Object Identifier: 10.11650/tjm.17.2013.3139

Subjects:
Primary: 37K05

Keywords: first-order Hamiltonian system , generalized Nehari manifold , ground state solutions , Homoclinic orbits

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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