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1

The existence of a unique solution of the hyperbolic functional differential equation

Karpowicz A.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

866--877

EN

We consider the Z. Szmydt problem for the hyperbolic functional differential equation. We prove a theorem on existence of a unique classical solution and the Carathéodory solution of the hyperbolic equation.

2

On some qualitative properties of mild solutions of nonlocal semilinear functional differential equations

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

854--865

EN

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

3

Boundary value problems for second order delay differential equations

Skóra L.

Opuscula Mathematica

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2012

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Vol. 32, no. 3

551-558

EN

We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order.

4

On a new type Bernstein-Stancu operators

Taşdelen, Başcanbaz-Tunca G., Erençin

Fasciculi Mathematici

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2012

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Nr 48

119--128

EN

In the present paper, firstly we obtain a functional differential equation corresponding to new type Bernstein-Stancu operators defined in [8]. Next we introduce some properties of these new type operators. In the end k-th order generalization of such operators is established.

5

On the Chaplygin method for the Darboux problem

Jaruszewska-Walczak D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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Vol. 47, [Z] 1

11-21

EN

In the paper we deal with the Darboux problem for hyperbolic functional differntial equations. We give the sufficient conditions for the existence of the sequence {z^(m)} such that if z is a classical solution of the original problem then {z^(m)} is uniformly convergent to z. The convergence that we get is of the Newton type.

6

Differential-functional Goursat problem

Wojciechowski R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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Vol. 47, [Z] 2

127-140

EN

This paper is devoted to a differential-functional Goursat problem for second-order hyperbolic equations. There are proved existence results based on the Banach and Schauder fixed point theorems with some Bielecki type norms.

7

Analytic solutions of a nonlinear functional differential equation with proportional delays

Si J.

Demonstratio Mathematica

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2000

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Vol. 33, nr 4

747-752

8

On the nonlocal boundary value problem for first order quasilinear partial functional differential equations

Człapiński T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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1999

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[Z] 39

57-73

EN

Quasilinear partial functional differential equations of the first order with nonlocal boundary condi-tions are considered. A theorem on the local existence and uniqueness of classical solutions is given. The method of bicharacteristics is used to transform the nonlocal boundary value problem into a functional integral equation and the Banach fixed-point principle to find its solution.

9

Note on an iterative functional differential equation

Si J., Cheng S.

Demonstratio Mathematica

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1998

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Vol. 31, nr 3

609-614

EN

This note is concerned with an iterative functional differential equation xI(z)=c1x(z) + . . . + Cmx(m) (z), where x(k) (z)=x(x(. . . x(z))) is the k-th iterate of the function x (z) . We apply the techniques developed in a previous paper [1] which deals with the simpler equation xI (z)=x (m) (z) and obtain analytic solutions for the more general equation.