Boundary value problems for first order functional differential equations with impulsive integral conditions

OSCILLATIONS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS GENERATED BY RETARDED ACTIONS

In this paper we study existence and uniqueness of solutions of boundary value problems for second order nonlinear delay differential equations. We transform the boundary value problem to an equivalent integral equation and then we use the Banach fixed point theorem and the notion of the Fréchet derivative.

Existence of solutions of non-autonomous second order functional differential equations with infinite delay

Anti-periodic boundary value problems for first order impulsive functional differential equations

The existence, uniqueness, and global attractivity of positive periodic solutions of first order functional differential equations is proved. Applications are made to fishing models, blood cell production (Hematopoiesis) models, Nicholson’s Blowflies model, and the Lasota-Wazewska model.

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.

An existence principle for boundary value problems for second order functional differential equations

Consider the delay – differential equation (1.1) − u ″ ( t ) = f ( t , u ( t ) , u t ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq3042.tif"/>

In this paper, we study the existence of periodic solutions for $n^{\text{th}}$ order functional differential equations $x^{ (n) } (t) +\sum\limits ^{n-1}_{i=0}b_{i}[x^{ (i) } (t) ]^{k}+ f (t, x (t-\tau) ) =p (t) $. Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of Mawhin.

The Green’s function is widely used in solving boundary value problems for differential equations, to which many mathematical and physical problems are reduced. In particular, solutions of partial differential equations by the Fourier method are reduced to boundary value problems for ordinary differential equations. Using the Green's function for a homogeneous problem, one can calculate the solution of an inhomogeneous differential equation. Knowing the Green's function makes it possible to solve a whole class of problems of finding eigenvalues in quantum field theory. The developed method for constructing the Green’s function of boundary value problems for ordinary linear differential equations is described. An algorithm and program for calculating the Green's function of boundary value problems for differential equations of the second and third orders in an explicit analytical form are presented. Examples of computing the Green's function for specific boundary value problems are given. The fundamental system of solutions of ordinary differential equations with singular points needed to construct the Green's function is calculated in the form of generalized power series with the help of the developed programs in the Maple environment. An algorithm is developed for constructing the Green's function in the form of power series for second-order and third-order differential equations with given boundary conditions. Compiled work programs in the Maple environment for calculating the Green functions of arbitrary boundary value problems for differential equations of the second and third orders. Calculations of the Green's function for specific third-order boundary value problems using the developed program are presented. The obtained approximate Green’s function is compared with the known expressions of the exact Green’s function and very good agreement is found

Periodic boundary value problems for delay differential equations with impulses

A unified approach to study the existence and numerical solution of functional differential equation

Study of singular boundary value problems for second order impulsive differential equations

Boundary value problem for first order impulsive functional integro-differential equations

Anti-periodic boundary value problems of second order impulsive differential equations