An anti-periodic LaSalle oscillation theorem for a class of functional differential equations. (English) Zbl 1166.34323

The author establishes a result on the existence of an anti-periodic solution for a class of functional differential equations which extends and improves known results.


34K11 Oscillation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
Full Text: DOI


[1] Okochi, H., On the existence of periodic solutions to nonlinear abstract parabolic equations, J. Math. Soc. Japan, 40, 3, 541-553 (1988) · Zbl 0679.35046
[2] Aftabizadeh, A. R.; Aizicovici, S.; Pavel, N. H., On a class of second-order anti-periodic boundary value problems, J. Math. Anal. Appl., 171, 301-320 (1992) · Zbl 0767.34047
[3] Aizicovici, S.; McKibben, M.; Reich, S., Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities, Nonlinear Anal., 43, 233-251 (2001) · Zbl 0977.34061
[4] Chen, Y.; Nieto, J. J.; ORegan, D., Anti-periodic solutions for fully nonlinear first-order differential equations, Mathematical and Computer Modelling, 46, 1183-1190 (2007) · Zbl 1142.34313
[5] Chen, T.; L iu, W.; Zhang, J.; Zhang, M., The Existence of anti-periodic solutions for Liénard equations, Journal of Mathematical Study, 40, 187-195 (2007), (in Chinese) · Zbl 1144.34335
[6] Delvos, F. J.; Knoche, L., Lacunary interpolation by antiperiodic trigonometric polynomials, BIT, 39, 439-450 (1999) · Zbl 0931.42003
[7] Du, J. Y.; Han, H. L.; Jin, G. X., On trigonometric and paratrigonometric Hermite interpolation, J. Approx. Theory, 131, 74-99 (2004) · Zbl 1064.42002
[8] Chen, H. L., Antiperiodic wavelets, J. Comput. Math., 14, 32-39 (1996) · Zbl 0839.42014
[9] Djiakov, P.; Mityagin, B., Spectral gaps of the periodic Schrodinger operator when its potential is an entire function, Adv. Appl. Math., 31, 562-596 (2003) · Zbl 1047.34100
[10] Djiakov, P.; Mityagin, B., Simple and double eigenvalues of the Hill operator with a two-term potential, J. Approx. Theory, 135, 70-104 (2005) · Zbl 1080.34066
[11] Cabada, A.; Vivero, D. R., Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations, Adv. Difference Equ., 4, 291-310 (2004) · Zbl 1083.39017
[12] Wang, Y.; Shi, Y. M., Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions, J. Math. Anal. Appl., 309, 56-69 (2005) · Zbl 1083.39019
[13] Abdurahman, A.; Anton, F.; Bordes, J., Half-string oscillator approach to string field theory (Ghost sector: I), Nuclear Phys. B, 397, 260-282 (1993)
[14] Ahn, C.; Rim, C., Boundary flows in general coset theories, J. Phys. A, 32, 2509-2525 (1999) · Zbl 0960.81062
[15] Kleinert, H.; Chervyakov, A., Functional determinants from Wronski Green function, J. Math. Phys., 40, 6044-6051 (1999) · Zbl 0963.34075
[16] Lasalle, J. L.; Lefshitz, S., Stability by Lyapunovs Direct Method with Application (1962), New York Academic Press
[17] Wu, R., An anti-periodic LaSalle oscillation theorem, Applied Mathematics Letters (2007)
[18] Cao, J.; Wang, J., Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. Circuits Syst.-I, 52, 5, 920-931 (2005) · Zbl 1374.34279
[19] Cao, J.; Wang, J., Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst.-I, 52, 2, 417-426 (2005) · Zbl 1374.93285
[20] Huang, H.; Cao, J.; Wang, J., Global exponential stability and periodic solutions of recurrent cellular neural networks with delays, Phys. Lett. A, 298, 5-6, 393-404 (2002) · Zbl 0995.92007
[21] Hale, J. K., Theory of Functional Differential Equations (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0425.34048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.