Maximum principles for periodic impulsive first order problems
Journal of Computational and Applied Mathematics - Special issue: positive solutions of nonlinear problems
Periodic boundary value problem for first-order impulsive functional differential equations
Journal of Computational and Applied Mathematics
Remarks on periodic boundary value problems for functional differential equations
Journal of Computational and Applied Mathematics
Monotone method for first-order functional differential equations
Computers & Mathematics with Applications
Preservation of oscillations of the Runge-Kutta method for equation x'(t)+ax(t)+a1x([t-1])=0
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Anti-periodic boundary value problems of second order impulsive differential equations
Computers & Mathematics with Applications
Impulsive anti-periodic boundary value problem of first-order integro-differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
An algorithm for approximate solving of differential equations with "maxima"
Computers & Mathematics with Applications
Boundary value problem for first order impulsive functional integro-differential equations
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
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This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differential equations with maximum and integro-differential equations. In this paper, we also prove that the Lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval. The corresponding results are established for the impulsive case. The general formulation includes several types of functional dependence (delay equations, equations with maxima, integro-differential equations). Finally, we consider the case of functional dependence which is given by nonincreasing and bounded functions.