Existence and uniqueness of anti-periodic solution for a kind of forced Rayleigh equation with state dependent delay and impulses

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 12, 2010, Pages 4076-4083

  Li, Yongkun ^a   Zhang, Tianwei ^a  

^a YUNNAN UNIVERSITY   (China)

Author keywords

Anti periodic solution; Coincidence degree; Impulse; Rayleigh equation; State dependent delay

Indexed keywords

ANTI-PERIODIC SOLUTIONS; COINCIDENCE DEGREE; EXISTENCE AND UNIQUENESS; IMPULSE; RAYLEIGH EQUATION; STATE DEPENDENT DELAY; STATE-DEPENDENT IMPULSE;

EQUATIONS OF STATE;

EID: 77952743633     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.01.023     Document Type: Article

References (39)

1. Lord Rayleigh Strutt J.W. Theory of sound vol. 1 (1877), Dover Publications, New York re-issued 1945
2. Burton T.A. Stability and periodic solutions of ordinary and functional differential equations (1985), Academic Press, Orland, FL
3. Hale J.K. Theory of functional differential equations (1977), Springer-Verlag, New York
4. Antosiewicz H.A. On nonlinear differential equations of the second order with integrable forcing term. J Lond Math Soc 30 (1955) 64-67
5. Sansone G., and Conti R. Non-linear differential equation (1964), MacMillan, New York
6. Lu S., and Gui Z. On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay. J Math Anal Appl 325 (2007) 685-702
7. Zong M., and Liang H. Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments. Appl Math Lett 206 (2007) 43-47
8. Zhang F., and Li Y. Existence and uniqueness of periodic solutions for a kind of duffing type p-Laplacian equation. Nonlinear Anal Real World Appl 9 (2008) 985-989
9. Chen H., Li K., and Li D. On the existence of exactly one and two periodic solutions of Linard equation. Acta Math Sin 47 3 (2004) 417-424 [in Chinese]
10. Gaines R.E., and Mawhin J. Coincidence degree and nonlinear differential equations. Lecture notes in mathematics vol. 568 (1977), Springer-Verlag, Berlin, New York
11. Deimling K. Nonlinear functional analysis (1985), Springer, Berlin
12. Gao H., and Liu B.W. Existence and uniqueness of periodic solutions for forced Rayleigh-type equations. Appl Math Comput 211 (2009) 148-154
13. Wang Y., and Zhang L. Existence of asymptotically stable periodic solutions of a Rayleigh type equation. Nonlinear Anal 71 (2009) 1728-1735
14. Zhou Y., and Tang X.H. On existence of periodic solutions of Rayleigh equation of retarded type. J Comput Appl Math 203 (2007) 1-5
15. Wang G.Q., and Cheng S.S. A priori bounds for periodic solutions of a delay Rayleigh equation. Appl Math Lett 12 (1999) 41-44
16. Okochi H. On the existence of periodic solutions to nonlinear abstract equations. J Math Soc Jpn 40 (1988) 541-553
17. Okochi H. On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains. Nonlinear Anal 14 (1990) 771-783
18. Chen Y. On Masseras theorem for anti-periodic solution, (English summary). Adv Math Sci Appl 9 1 (1999) 125-128
19. Yin Y. Monotone iterative technique and quasilinearization for some anti-periodic problems. Nonlinear World 3 2 (1996) 253-266
20. Yin Y. Remarks on first order differential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2 1 (1995) 83-94
21. Aftabizadeh A.R., Aizicovici S., and Pavel N.H. On a class of second-order anti-periodic boundary value problems. J Math Anal Appl 171 (1992) 301-320
22. Aizicovici S., McKibben M., and Reich S. Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal 43 (2001) 233-251
23. Chen Y., Nieto J.J., and O'regan D. Anti-periodic solutions for fully nonlinear first-order differential equations. Math Comput Modell. 46 (2007) 1183-1190
24. Chen T., Liu W., Zhang J., and Zhang M. The existence of anti-periodic solutions for Linard equations. J Math Study 40 (2007) 187-195 [in Chinese]
25. Delvos F.J., and Knoche L. Lacunary interpolation by antiperiodic trigonometric polynomials. BIT 39 (1999) 439-450
26. Du J.Y., Han H.L., and Jin G.X. On trigonometric and paratrigonometric Hermite interpolation. J Approx Theory 131 (2004) 74-99
27. Chen H.L. Antiperiodic wavelets. J Comput Math 14 (1996) 32-39
28. Akca H., Alassar R., Covachev V., Covacheva Z., and Al-Zahrani E. Continuous-time additive Hopfield-type neural networks with impulses. J Math Anal Appl 290 (2004) 436-451
29. Gopalsamy K. Stability of artificial neural networks with impulses. Appl Math Comput 154 (2004) 783-813
30. Guan Z.H., James L., and Chen G. On impulsive autoassociative neural networks. Neural Netw 13 (2000) 63-69
31. Liu X., and Xu B. Exponential stability of impulsive high-order Hopfield type neural networks with time varying delays. IEEE Trans Neural Netw 16 (2005) 1329-1339
32. Zhang Y., and Sun J.T. Stability of impulsive neural networks with delays. Phys Lett A 348 (2005) 44-50
33. Li Y.K., Xing W.Y., and Lu L.H. Existence and global exponential stability of periodic solution of a class of neural networks with impulses. Chaos Solitons Fractals 27 (2006) 437-445
34. Li Y.K., Chen X.R., and Zhao L. Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales. Neurocomputing 72 (2009) 1621-1630
35. Sun J.S., Zhang Y., and Wu Q.D. Less conservative conditions for asymptotic stability of impulsive control systems. IEEE Trans Auto Control 48 (2003) 829-831
36. Yang Z.C., and Xu D.Y. Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays. Appl Math Comput 177 (2006) 63-78
37. Liang J.L. Global exponential stability of impulsive high-order BAM neural networks with timevarying delays. Neural Netw 19 (2006) 1581-1590
38. Bai C. Stability analysis of Cohen-Grossberg BAM neural networks with delays and impulses. Chaos Solitons Fractals 35 (2008) 263-267
39. O'regan D., Cho Y.J., and Chen Y.Q. Topological degree theory and application (2006), Taylor & Francis Group, Boca Raton, London, New York