JOURNAL BROWSE
Search
Advanced SearchSearch Tips
EXISTENCE OF PERIODIC SOLUTIONS FOR PLANAR HAMILTONIAN SYSTEMS AT RESONANCE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
EXISTENCE OF PERIODIC SOLUTIONS FOR PLANAR HAMILTONIAN SYSTEMS AT RESONANCE
Kim, Yong-In;
  PDF(new window)
 Abstract
The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar map is identically zero.
 Keywords
planar Hamilton system;resonance;periodic solution;
 Language
English
 Cited by
1.
On homoclinic orbits for a class of damped vibration systems, Advances in Difference Equations, 2012, 2012, 1, 102  crossref(new windwow)
2.
Non-periodic damped vibration systems with sublinear terms at infinity: Infinitely many homoclinic orbits, Nonlinear Analysis: Theory, Methods & Applications, 2013, 92, 168  crossref(new windwow)
3.
Ground state homoclinic orbits of superquadratic damped vibration systems, Advances in Difference Equations, 2014, 2014, 1, 230  crossref(new windwow)
4.
Multiple Homoclinics for Nonperiodic Damped Systems with Superlinear Terms, Bulletin of the Malaysian Mathematical Sciences Society, 2016  crossref(new windwow)
5.
Ground state homoclinic orbits of damped vibration problems, Boundary Value Problems, 2014, 2014, 1, 106  crossref(new windwow)
6.
Nonperiodic Damped Vibration Systems with Asymptotically Quadratic Terms at Infinity: Infinitely Many Homoclinic Orbits, Abstract and Applied Analysis, 2013, 2013, 1  crossref(new windwow)
 References
1.
J. M. Alonso and R. Ortega, Roots of unity and unbounded motions of an asymmetric oscillator, J. Differential Equations 143 (1998), no. 1, 201-220. crossref(new window)

2.
A. Capietto, W. Dambroslo, and Z. Wang, Coexistence of unbounded and periodic so-lutions to perturbed damped isochronous oscillators at resonance, Proc. Roy. Soc. Edin-burgh Sect. A 138 (2008), no. 1, 15-32.

3.
A. Capietto and Z. Wang, Periodic solutions of Lienard equations with asymmetric nonlinearities at resonance, J. London Math. Soc. (2) 68 (2003), no. 1, 119-132. crossref(new window)

4.
T. Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918-931.

5.
C. Fabry and A. Fonda, Nonlinear resonance in asymmetric oscillators, J. Differential Equations 147 (1998), no. 1, 58-78.

6.
C. Fabry and J. Mawhin, Oscillations of a forced asymmetric oscillator at resonance, Nonlinearity 13 (2000), no. 3, 493-505. crossref(new window)

7.
A. Fonda, Positively homogeneous Hamiltonian systems in the plane, J. Differential Equations 200 (2004), no. 1, 162-184. crossref(new window)

8.
A. Fonda and J. Mawhin, Planar differential systems at resonance, Adv. Differential Equations 11 (2006), no. 10, 1111-1133.

9.
N. G. Lloyd, Degree Theory, University Press, Cambridge, 1978.

10.
J. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457-475. crossref(new window)

11.
R. Ortega, Asymmetric oscillators and twist mappings, J. London Math. Soc. (2) 53 (1996), no. 2, 325-342. crossref(new window)

12.
Z.Wang, Coexistence of unbounded solutions and periodic solutions of Lienard equations with asymmetric nonlinearities at resonance, Sci. China Ser. A 50 (2007), no. 8, 1205-1216. crossref(new window)

13.
X. Yang, Unboundedness of solutions of planar Hamiltonian systems. Differential & difference equations and applications, 1167-1176, Hindawi Publ. Corp., New York, 2006.