Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems

Yanheng Ding; Cheng Lee

doi:10.1016/j.na.2008.10.116

Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems

Yanheng Ding, Cheng Lee

Department of Mathematics

Research output: Contribution to journal › Article

46 Citations (Scopus)

Abstract

In this paper, we find new conditions, which are different from those used in previous related studies, to ensure the existence of infinitely many homoclinic orbits for the second order Hamiltonian systems of the form - over(q, ̈) = V_q (t, q) . Here, we assume that V (t, q) depends periodically on t, and assume, on q, that V (t, q) is asymptotically quadratic at q = 0 and is, as | q | → ∞, either asymptotically quadratic or superquadratic, as well as the new conditions.

Original language	English
Pages (from-to)	1395-1413
Number of pages	19
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
Issue number	5-6
DOIs	https://doi.org/10.1016/j.na.2008.10.116
Publication status	Published - 2009 Sep 1

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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abstract = "In this paper, we find new conditions, which are different from those used in previous related studies, to ensure the existence of infinitely many homoclinic orbits for the second order Hamiltonian systems of the form - over(q,{\" }) = Vq (t, q) . Here, we assume that V (t, q) depends periodically on t, and assume, on q, that V (t, q) is asymptotically quadratic at q = 0 and is, as | q | → ∞, either asymptotically quadratic or superquadratic, as well as the new conditions.",

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AB - In this paper, we find new conditions, which are different from those used in previous related studies, to ensure the existence of infinitely many homoclinic orbits for the second order Hamiltonian systems of the form - over(q, ̈) = Vq (t, q) . Here, we assume that V (t, q) depends periodically on t, and assume, on q, that V (t, q) is asymptotically quadratic at q = 0 and is, as | q | → ∞, either asymptotically quadratic or superquadratic, as well as the new conditions.

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