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Boundedness of solutions of a nonlinear nonautonomous neutral delay equation. (English) Zbl 0731.34089
The neutral type difference differential equation $$ x'(t)\quad =\quad r(t)x(t) [a(t)-x(t-1)-c(t)x'(t-1)] $$ arising in population dynamics is considered. Conditions of boundedness and unboundedness of solutions of the Cauchy problem for this equation formulated in terms of coefficients and initial data are given.

34K40Neutral functional-differential equations
34K99Functional-differential equations
Full Text: DOI
[1] Cooke, K. L.; Den Driessche, P. Van: On zeroes of some transcendental equations. Funkcial. ekvac. 29, 77-90 (1986) · Zbl 0603.34069
[2] Cooke, K. L.; Grossman, Z.: Discrete delay, distributed delay and stability switches. J. math. Anal. appl. 86, 592-627 (1982) · Zbl 0492.34064
[3] Freedman, H. I.; Kuang, Y.: Stability switches in linear scalar neutral delay equations. Funkcial. ekvac. 34 (1991) · Zbl 0749.34045
[4] Gopalsamy, K.: On the global attractivity in a generalised delay logistic differential equation. Math. proc. Cambridge philos. Soc. 100, 183-192 (1986) · Zbl 0622.34080
[5] Gopalsamy, K.; Kulenovic, M. R. S; Ladas, G.: Time lags in a ”food-limited” population model. Appl. anal. 31, 225-237 (1988) · Zbl 0639.34070
[6] Gopalsamy, K.; Zhang, B. G.: On a neutral delay-logistic equation. Dynamics stability systems 2, 183-195 (1988) · Zbl 0665.34066
[7] Haddock, J. R.; Terjéki, J.: Liapunov-razumikhin functions and an invariance principle for functional differential equations. J. differential equations 48, 95-122 (1983) · Zbl 0531.34058
[8] Hale, J. K.: Behavior near constant solutions of functional differential equations. J. differential equations 15, 278-294 (1974) · Zbl 0273.34049
[9] Hale, J. K.: Theory of functional differential equations. (1977) · Zbl 0352.34001
[10] Hale, J. K.: Asymptotic behavior of dissipative systems. Mathematics surveys and monographs (1988) · Zbl 0642.58013
[11] Pielou, E. C.: Mathematical ecology. (1977) · Zbl 0259.92001