The Existence of Homoclinic Solutions for Second Order Differential Equation

Jie Gao

doi:10.4028/www.scientific.net/AMM.195-196.728

Paper Titles

Lattice Boltzmann Simulation of High Reynolds Number Flow around Blade Hydrofoil of Tidal Current Energy Conversion Device
p.705

Heat Conduction Equation Finite Volume Method to Achieve on MATLAB
p.712

A Hybrid Process Modeling Method and its Application in Equipment Support System
p.718

Real-Time Flame Simulation Based on GPU
p.723

The Existence of Homoclinic Solutions for Second Order Differential Equation
p.728

Simulation of a Single-Radio Multi-Channel Vehicular Node Structure for VANET in NS-2
p.732

Simulation for Mixture of Archimedean Copulas
p.738

Simulation and Performance Analysis of FH Spread Spectrum Communication System under Repeater Jamming
p.744

Simulation of Novel Three-Level Shunt Active Power Filter
p.748

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 195-196The Existence of Homoclinic Solutions for Second...

The Existence of Homoclinic Solutions for Second Order Differential Equation

Abstract:

The research for Hamilton system is a classical problem, it has valuable applications in celestial mechanics, plasma physics, and biological engineering. But in actual management, Hamilton system can be changed into solving homoclinic solutions of differential equation or system. This paper studies the existence of homoclinic solutions for a class of second order differential equation, we will prove this equation exists at least one nontrivial homoclinic solution.

You might also be interested in these eBooks

Mechanical Engineering and Intelligent Systems

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 195-196)

Pages:

728-731

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.195-196.728

Citation:

Cite this paper

Online since:

August 2012

Authors:

Jie Gao

Keywords:

(PS) Condition, Critical Point, Hilbert Space, Homoclinic Solution

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] H. Poincaré, les méthodes nouvelles de la mécanique céleste, Gauthier-villars, pairs, pp.1897-1899.

Google Scholar

[2] E. Paturel, Multiple homoclinic orbits for a class of Hamiltonian systems, Calc. Val. Partial Differential Equations, 12(2001), no. 2, pp.117-143.

DOI: 10.1007/pl00009909

Google Scholar

[3] Y. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Anal. 25 (11)(1995), pp.1095-1113.

DOI: 10.1016/0362-546x(94)00229-b

Google Scholar

[4] X. Tang and X. Lin, Homoclinic solutions for a class of second order Hamiltonian systems, J. Math. Anal. Appl. 354 (2) (2009), pp.539-549.

DOI: 10.1016/j.jmaa.2008.12.052

Google Scholar

[5] Q. Zhang and C. Liu, Infinitely many homoclinic solutions for second order Hamiltonian systems, Nonlinear Anal., 72(2010), pp.894-903.

DOI: 10.1016/j.na.2009.07.021

Google Scholar

[6] Z. Zhang and R. Yuan, Homoclinic solutions of some second order non-autonomous systems, Nonlinear Analysis, 71(2009), pp.5790-5798.

DOI: 10.1016/j.na.2009.05.003

Google Scholar

[7] W. Omana and M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differential Integral Equations, 5(1992), no. 5, pp.1115-1120.

DOI: 10.57262/die/1370870945

Google Scholar

[8] I. Ekeland, Convexity Methods in Hamiltonian Mechanics, 19, Springer-Verlag, Berlin, (1990).

Google Scholar