Hostname: page-component-7f64f4797f-l842n Total loading time: 0 Render date: 2025-11-04T01:00:01.764Z Has data issue: false hasContentIssue false
  • English
  • Français

Smooth solutions of a nonhomogeneous iterative functional differential equation

Published online by Cambridge University Press:  14 November 2011

Jian-Guo Si  and
Sui Sun Cheng
Jian-Guo Si
Affiliation:
Department of Mathematics, Binzhou Normal College, Binzhou, Shandong, 256604, P.R. China
Sui Sun Cheng
Affiliation:
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with an iterative functional differential equation x(t) = c1x(t) + c2x[2](t) + … cmχ[m](t) + F(t), where x[i](t) is the i-th iterate of the function x(t). By means of Schauder's Fixed Point Theorem, we establish a local existence theorem for smooth solutions which also depend continuously on the forcing function F(t).

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 821 - 831
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Cooke, K. L.. Functional differential systems: some models and perturbation problems. In Proceedings of the International Symposium on Differential Equations and Dynamical Systems, Puerto Rico, 1965 (New York: Academic Press, 1967).Google Scholar
2Eder, E.. The functional differential equation x´(t) = x(x(t)). J. Differential Equations 54 (1984), 390–400.CrossRefGoogle Scholar
3Feckan, E.. On certain type of functional differential equations. Math. Slovaca 43 (1993), 39–43.Google Scholar
4Shi, B. and Li, Z. X.. Existence of solutions and bifurcation of a class of first-order functional differential equations. Ada Math. Appl. Sinica 18 (1995), 83–9.Google Scholar
5Shi, B., Wang, Z. C. and Li, Z. X.. Asymptotic behavior of the solutions of a class of new type of functional differential equations. J. Hunan Univ. 23(2) (1996), 1–5.Google Scholar
6Si, J. G., Li, W. R. and Cheng, S. S.. Analytic solutions of an iterative functional differential equation. Comp. Math. Appl. 33 (6) (1997), 47–51.CrossRefGoogle Scholar
7Stanek, S.. On global properties of solutions of functional differential equations x´(t) = x(x(t)) + x(t). Dynam. Systems Appl. 4 (1995), 263–78.Google Scholar
8Stephan, B. H.. On the existence of periodic solutions of z´(t)=–az(t–r + µk(t,z(t))) +F(t). J. Differential Equations 6 (1969), 408–19.CrossRefGoogle Scholar
9Wang, K.. On the equation x´(t) = f(x(x(t))). Funkcial. Ekvac. 33 (1990), 405–25.Google Scholar
10Wu, H. Z.. A class of functional differential equations with deviating arguments depending on the state. Ada Math. Sinica 38 (6) (1995), 803–9.Google Scholar