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Asymptotic behavior and oscillation of functional differential equations. (English) Zbl 1113.34059
The author is concerned with the comparison of the solutions of the linear autonomuous functional differential equation $$x'(t)= Lx_t\tag*$$ and the perturbed equation $$x'(t)= Lx_t+ f(t, x_t),\text{ where }f: [\sigma_0,\infty)\times \bbfC\to \bbfC^n\tag{**}$$ is a continuous function and $x_t$ is defined by $x_t(s)= x(t+ s)$ for $-r\le s\le 0$. The present paper is the continuation of the author’s results in [J. Math. Anal. Appl. 316, No. 1, 24--41 (2006; Zbl 1102.34060)].

34K25Asymptotic theory of functional-differential equations
34K11Oscillation theory of functional-differential equations
34K06Linear functional-differential equations
Full Text: DOI
[1] Cao, Y.: The discrete Lyapunov function for scalar delay differential equations. J. differential equations 87, 365-390 (1990) · Zbl 0717.34086
[2] Coppel, W. A.: Stability and asymptotic behavior of differential equations. (1965) · Zbl 0154.09301
[3] Diekman, O.; Van Gils, S. A.; Verduyn-Lunel, S. M.; Walther, H. -O.: Delay equations, functional-, complex-, and nonlinear analysis. (1995) · Zbl 0826.34002
[4] Elbert, Á.; Stavroulakis, I. P.: Oscillation and nonoscillation criteria for delay differential equations. Proc. amer. Math. soc. 123, 1503-1510 (1995) · Zbl 0828.34057
[5] Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics. (1992) · Zbl 0752.34039
[6] Győri, I.; Ladas, G.: Oscillation theory of delay differential equations with applications. (1991)
[7] Győri, I.; Trofimchuk, S.: On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation. Nonlinear anal. 48, 1033-1042 (2002) · Zbl 1007.34063
[8] Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[9] Kappel, F.; Wimmer, H. K.: An elementary divisor theory for autonomous linear functional differential equations. J. differential equations 21, 134-147 (1976)
[10] Krisztin, T.; Arino, O.: The two-dimensional attractor of a differential equation with state-dependent delay. J. dynam. Differential equations 13, 453-522 (2001) · Zbl 1016.34075
[11] Kulenovic, M. R. S.; Ladas, G.; Meimaridou, A.: On oscillation of nonlinear delay differential equations. Quart. appl. Math. 45, 155-164 (1987) · Zbl 0627.34076
[12] Li, B.: Oscillations of delay differential equations with variable coefficients. J. math. Anal. appl. 192, 312-321 (1995) · Zbl 0829.34060
[13] Mallet-Paret, J.: Morse decomposition for delay-differential equations. J. differential equations 72, 270-315 (1988) · Zbl 0648.34082
[14] Mallet-Paret, J.: The Fredholm alternative for functional differential equations of mixed type. J. dynam. Differential equations 11, 1-47 (1999) · Zbl 0927.34049
[15] Mallet-Paret, J.: The global structure of travelling waves in spatially discrete dynamical systems. J. dynam. Differential equations 11, 49-127 (1999) · Zbl 0921.34046
[16] Pituk, M.: The hartman -- wintner theorem for functional differential equations. J. differential equations 155, 1-16 (1999) · Zbl 0929.34057
[17] M. Pituk, A Perron type theorem for functional differential equations, J. Math. Anal. Appl., in press · Zbl 1102.34060