Asymptotic estimate for differential equation with power coefficients and power delays

Petr Kundrát

doi:10.2478/v10127-011-0009-1

.blurhash-client-img { display: none !important; }

Asymptotic estimate for differential equation with power coefficients and power delays

Tatra Mountains Mathematical Publications

Volume 48 (2011): Issue 1 (April 2011)

By: Petr Kundrát

Open Access

|Nov 2012

Abstract

The paper analyzes the asymptotic bounds of solutions of differential equation with power coefficients, power delays and a forcing term in the form , where a₀ is a negative real, λ₀ = 1 and . Some additional assumptions on power coefficients and a forcing term f(t) are considered to obtain an asymptotic estimate for solutions of the studied differential equation. The application of the result is illustrated by several examples.

References

[1] ˇC ERM´AK, J.-KUNDR´AT, P.: Linear differential equations with unbounded delays and a forcing term, Abstr. Appl. Anal. 2004 (2004), 337-345.10.1155/S1085337504306020
Search in Google Scholar
[2] ˇC ERM´AK, J.: On the differential equation with power coefficients and proportional de- lays, Tatra Mt. Math. Publ. 38 (2007), 57-69.
Search in Google Scholar
[3] DERFEL, G.-VOGL, F.: On the asymptotics of solutions of a class of linear functional- -differential equations, European J. Appl. Math. 7 (1996), 511-518.10.1017/S0956792500002527
Search in Google Scholar
[4] HEARD, M. L.: A change of variables for functional differential equations, J. Differential Equations 18 (1975), 1-10.10.1016/0022-0396(75)90076-5
Search in Google Scholar
[5] ISERLES, A.: On the generalized pantograph functional-differential equation, European J. Appl. Math. 4 (1993), 1-38.10.1017/S0956792500000966
Search in Google Scholar
[6] ISERLES, A.: Exact and discretized stability of the pantograph equation, Appl. Numer. Math. 24 (1997), 295-308.10.1016/S0168-9274(97)00027-5
Search in Google Scholar
[7] LIU, Y.: Asymptotic behaviour of functional-differential equations with proportional time delays, European J. Appl. Math. 7 (1996), 11-30.10.1017/S0956792500002163
Search in Google Scholar
[8] MAKAY, G.-TERJ´ EKI, J.: On the asymptotic behaviour of the pantograph equations, Electron. J. Qual. Theory Differ. Equ. 2 (1998), 1-12.10.14232/ejqtde.1998.1.2
Search in Google Scholar
[9] NEUMAN, F.: Simultaneous solutions of a system of Abel equations and differential equations with several deviations, Czechoslovak Math. J. 32(107) (1982), 488-494.10.21136/CMJ.1982.101824
Search in Google Scholar