Time delays occur in differential equation arising in many fields of applied mathematics: chemistry, ecology, biology, population dynamics, electric engineering. In population dynamics they may model the gestation or maturation time of a species, or time taken for food resources to regenerate. The purpose of this paper is to study the dependence on parameter for a differential system with delays from population dynamics using the theory of weakly Picard operators. The theory of weakly Picard operators is very useful in studying the properties of the solution of Volterra integral equations.
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
D. Otrocol, Smooth dependence on paramters for a differential equation with delay from population dynamics, 2007 International Conference on Engineering and Mathematics, Bilbao, July 9-11, 2007, pp. 3-10.
see the expansion block below.
 Muresan, I., Functional-Integral Equations, Mediamira, Romania, 2003.
 Otrocol, D., Data Dependence for the Solution of a Lotka-Volterra System with two Delays, Mathematica, vol. 48, 71, 1, 61-68, 2006.
 Otrocol, D., Lotka-Volterra System with two Delays via Wealky Picard Operators, Nonlinear Analysis Forum, 10, 2, 193-199, 2005.
 Rus, I. A., Generalized Contractions, Seminar of Fixed Point Theory, “Babs-Bolyai” University, 1-130, 1983.
 Rus, I. A., Functional-Differential Equation of Mixed Type, via Weakly Picard Operators, Seminar of Fixed Point Theory, vol. 3, 335-346, 2002.
 Rus, I. A., Generalized Contractions and Applications, Cluj University Press, Romania, 2001.
 Rus, I. A., Principles and Applications of the Fixed Point Theory, Dacia, Romania, 1979.
 Serban, M. A., Fiber ϕ-Contractions, Studia Univ. “Babs-Bolyai”, Mathematica, 44, 3, 99-108, 1999.