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.
| 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 | |
| Publication status | Published - 2009 Sep 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
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Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems. / Ding, Yanheng; Lee, Cheng.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 71, No. 5-6, 01.09.2009, p. 1395-1413.Research output: Contribution to journal › Article
TY - JOUR
T1 - Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems
AU - Ding, Yanheng
AU - Lee, Cheng
PY - 2009/9/1
Y1 - 2009/9/1
N2 - 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.
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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UR - http://www.scopus.com/inward/citedby.url?scp=65549101794&partnerID=8YFLogxK
U2 - 10.1016/j.na.2008.10.116
DO - 10.1016/j.na.2008.10.116
M3 - Article
VL - 71
SP - 1395
EP - 1413
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 5-6
ER -