Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Graef, L. Kong (2011)
Periodic solutions of first order functional differential equationsAppl. Math. Lett., 24
Ruyun Ma, Ruipeng Chen, Tianlan Chen (2011)
Existence of positive periodic solutions of nonlinear first-order delayed differential equationsJournal of Mathematical Analysis and Applications, 384
Yongkun Li, Jianwen Zhou (2010)
Existence of Solutions for a Class of Damped Vibration Problems on Time ScalesAdvances in Difference Equations, 2010
T. Bartsch, Yanheng Ding (2006)
Deformation theorems on non‐metrizable vector spaces and applications to critical point theoryMathematische Nachrichten, 279
P. Rabinowitz (1986)
Minimax methods in critical point theory with applications to differential equations
(1985)
Circulantmatrices and differential delay equations
Xi-Lan Liu, Wan-Tong Li (2004)
Existence and uniqueness of positive periodic solutions of functional differential equationsJournal of Mathematical Analysis and Applications, 293
S. Cheng, Guang Zhang (2001)
Existence of Positive Periodic Solutions for Non-Autonomous Functional Differential Equations
G.Stephen Jones (1962)
The existence of periodic solutions of f′(x) = − αf(x − 1){1 + f(x)}Journal of Mathematical Analysis and Applications, 5
GS Jones (1962)
The existence of periodic solutions of $$f ^{\prime }(x) = af (x - 1)[1 + f (x)]$$ f ′ ( x ) = a f ( x - 1 ) [ 1 + f ( x ) ]J. Math. Anal. Appl., 5
R. Nussbaum (1978)
A Hopf global bifurcation theorem for retarded functional differential equationsTransactions of the American Mathematical Society, 238
Haiyan Wang (2004)
Positive periodic solutions of functional differential equationsJournal of Differential Equations, 202
J. Mallet-Paret, G. Sell (1996)
Systems of Differential Delay Equations: Floquet Multipliers and Discrete Lyapunov FunctionsJournal of Differential Equations, 125
Yanheng Ding, Cheng Lee (2000)
Periodic Solutions of Hamiltonian SystemsSIAM J. Math. Anal., 32
Zhiming Guo, Jianshe Yu (2005)
Multiplicity results for periodic solutions to delay differential equations via critical point theoryJournal of Differential Equations, 218
Xian Wu, Shaoxiong Chen, K. Teng (2008)
On variational methods for a class of damped vibration problemsNonlinear Analysis-theory Methods & Applications, 68
Zhi-Long Jin, Haiyan Wang (2010)
A note on positive periodic solutions of delayed differential equationsAppl. Math. Lett., 23
PH Rabinowitz (1978)
Periodic solutions of Hamiltonian systemsCommun. Pure Appl. Math., 31
J. Mawhin, M. Willem (1989)
Critical Point Theory and Hamiltonian Systems
R. Agarwal, V. Otero-Espinar, K. Perera, D. Vivero (2006)
Basic properties of Sobolev's spaces on time scalesAdvances in Difference Equations, 2006
Jianwen Zhou, Yongkun Li (2010)
Existence of solutions for a class of second-order Hamiltonian systems with impulsive effectsNonlinear Analysis-theory Methods & Applications, 72
Ke-qing Wu, X. Wu (2012)
Multiplicity results of periodic solutions for a class of first order delay differential equations ✩
(1974)
Ordinary differential equations which yield periodic solution of delay equations
G. Guseinov (2003)
Integration on time scalesJournal of Mathematical Analysis and Applications, 285
J. Mallet-Paret, G. Sell (1996)
THE POINCARE-BENDIXSON THEOREM FOR MONOTONE CYCLIC FEEDBACK SYSTEMS WITH DELAYJournal of Differential Equations, 125
T. Furumochi, K. Hale (1979)
Existence of periodic solutions of two-dimensional differential-delay equationsApplicable Analysis, 9
Jianwen Zhou, Yongkun Li (2010)
Sobolev’s spaces on time scales and its applications to a class of second order Hamiltonian systems on time scalesNonlinear Analysis-theory Methods & Applications, 73
In this paper, we present a recent approach via variational methods and critical point theory to obtain the existence of periodic solutions for a class of delay Hamiltonian systems on time scales with impulsive effects. The variational principle is given, and some existence theorems and two multiplicity results of periodic solutions are obtained. Finally, one example is presented to illustrate the feasibility and effectiveness of our results. Our results are new even in both the differential equations case and the difference equations case.
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Jul 2, 2015
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.