A Picard theorem for iterative differential equations

• Autorzy: Li W. , Cheng S.
• Języki publikacji: EN

Abstrakty

EN

A Picard type existence and uniqueness theorem is established for iterative differential equations of the form y'(x) - f(x,y(h(x) + g (y (x)))), a special case of which is y'(x) = f(x,y(y(x))). Such iterative differential equations can be used to model infective disease processes, pattern formation in the plane, and in investigations of dynamical systems.

Słowa kluczowe

EN

Picard theorem; differential equations

PL

twierdzenie Picarda; równania różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 2
• Strony: 371--380
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Li W.

autor

Cheng S.

• Department of Mathematics Binzhou University Binzhou, Shangdong 256600. P.R. China

Bibliografia

• [1] E. Eder, The functional differential equation x'(t)=x(x(t)), J. Differential Equations 54 (1984), 390–400.
• [2] S. S. Cheng, Smooth Solutions of Iterative Functional Differential Equations, 2004-Dynamical Systems and Application, eds. H. Akca, A. Boucherif and V. Covachev, GBS Publishers & Distributions, 2005.
• [3] W. R. Li, S. S. Cheng, T. T. Lu, Closed form solutions of iterative functional differential equations, Appl. Math. E-Notes 1 (2001), 1–4.
• [4] A. Pelczar, On some iterative differential equations I, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Prace Matematyczne, 12 (1968), 53–56.
• [5] R. D. Driver, A two-body problem of classical electrodynamics: the one-dimensional case, Ann. Physics 21 (1963), 122–142.
• [6] R. D. Driver, Can the future influence the present? Phys. Rev. D. 19 (4) (1979), 1098–1107.
• [7] K. L. Cooke, Functional differential systems: some models and perturbation problems, Inter. Symp. Diff. Eqs. Dynamical Systems, Puerto Rico, 1965.
• [8] W. X. Yang, W. G. Ge, Periodic solutions for the differential-iterative equation x'+g(x(x))=p(t) (in Chinese) J. Beijing Inst. Technol. (Chin. Ed.) 22 (5) (2002), no. 5, 537–539.