Wyniki wyszukiwania - BazTech

1

On the quasilinear Cauchy problem for a hyperbolic functional differential equation

Puźniakowska-Gałuch E.

Opuscula Mathematica

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2015

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Vol. 35, no. 6

915--933

EN

The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.

2

Oscillation results for higher order nonlinear neutral differential equations with positive and negative coefficients

Panigrahi S, Basu R.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

109--121

EN

In this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [5]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.

3

Existence and regularity of solutions for hyperbolic functional differential problems

Kamont Z.

Opuscula Mathematica

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2014

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Vol. 34, no. 2

217--242

EN

A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is proved by using a method of successive approximations. We show a theorem on the differentiability of solutions with respect to initial functions which is the main result of the paper.

4

Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions

Czernous W., Jaruszewska-Walczak D.

Opuscula Mathematica

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2014

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Vol. 34, no. 2

311--326

EN

We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.

5

Oscillatory and asymptotic behavior of fourth order nonlinear neutral delay differential equations with positive and negative coefficients

Tripathy A. K., Panigrahi S, Basu R

Fasciculi Mathematici

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2014

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Nr 52

155--174

EN

In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) = 0 and (NH) (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) =f (t) are studied under the assumption ...[wzór] for various ranges of p(t). Using Schauder’s fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of (NH).

6

Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations

Netka M.

Opuscula Mathematica

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2009

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Vol. 29, no. 1

69-79

EN

The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.

7

Functional differential equations of second order

Skóra L.

Czasopismo Techniczne. Nauki Podstawowe

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2009

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R. 106, z. 1-NP

63-75

EN

In this article, we present some results on the existence and uniqueness of the solutions of boundary value problem for functional differential equations of second order.

PL

Artykuł zawiera wyniki dotyczące istnienia i jednoznaczności rozwiązań zagadnienia brzegowego dla równań różniczkowo-funkcjonalnych drugiego rzędu.

8

Numerical methods for hyperbolic differential functional problems

Ciarski R.

Opuscula Mathematica

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2008

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Vol. 28, no. 1

29-46

EN

The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.

9

On the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators

Sremr J.

Fasciculi Mathematici

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2007

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Nr 37

87-108

EN

We establish new efficient conditions sufficient for the unique solvability of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators.

10

Implicit difference methods for Hamilton-Jacobi differential functional equations

Kępczyńska A.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

125-150

EN

Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference functional equations. The numerical methods are difference schemes which are implicit with respect to time variable. A complete convergence analysis for the methods is given and it is shown that the new methods are considerable better than the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type. Numerical examples are given.

11

Numerical approximations of parabolic functional differential equations on unbounded domains

Baranowska A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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Vol. 47, [Z] 2

193-205

EN

The paper is concerned with initial problems for nonlinear parabolic functional differential equations. A general class of difference methods is constructed. A theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of several variables is presented. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given function satisfy nonlinear estimates of the Perron type with respect to a functional variable. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables. Numerical examples are presented.

12

Darboux problem with a discontinuous right-hand side

Pikuta B.

Journal of Applied Analysis

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2006

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Vol. 12, nr 1

147-152

EN

We prove an existence theorem for the Darboux problem [wzór], where g is bounded and measurable.

13

On the extension of Lie group analysis to functional differential equations

Oberlack M., Wacławczyk M.

Archives of Mechanics

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2006

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Vol. 58, nr 6

597-618

EN

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations. In order to perform the group analysis and deal with the functional derivatives, we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example, the procedure is applied to the functional formulation of the Burgers equation. The method can further lead to important applications in continuum mechanics.

14

On extremal solutions of differential equations with advanced argument

Augustynowicz A., Jankowski J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2006

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Vol. 46, [Z] 1

17-24

EN

We obtain existence of absolutely continuous extremal solutions of the problem u'(x) = F(x, u(x), u(h(x))), u(0) = u0, and the Darboux problem for u_xy(x, y) = G(x, y, u(x, y), u(H(x, y))), where h and H are arbitrary continuous deviated arguments.

15

Numerical approximations of difference functional equations and applications

Kamont Z.

Opuscula Mathematica

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2005

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Vol. 25, no. 1

109-130

EN

We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

16

On a functional-differential equation (in a historical context)

Pelczar A.

Opuscula Mathematica

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1999

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Vol. 19

45-61

EN

The paper consists of two parts. The first one presents some historical remarks concerning the beginning of the modern mathematics in Kraków (and - more general - in the whole territory of Poland) at the end of the XIX-th century and further survey of it during the XX-th century. Some special aspects (like, for instance, connections between mathematics and applications as there were seen by prominent mathematicians, founders and members of Kraków scientific schools) of the history of research and teaching in mathematics, are mentioned. The second part deals with a functional-differential equations generalizing an integro-differential equation which was investigated by J. Bodziony, S. Gołąb and J. Szarski in connections with some technical problems arising when screening certain granular bodies.

PL

Praca składa się z dwóch części. Pierwsza z nich prezentuje pewne uwagi historyczne dotyczące początków współczesnej matematyki w Krakowie (i szerzej - na wszystkich ziemiach polskich) przy końcu wieku XIX-go i jej późniejszego rozwoju w wieku XX-tym. Pewne specjalne aspekty (takie, jak np. związki między matematyką i zastosowaniami, tak jak były one widziane przez wybitnych matematyków, tworzących krakowskie szkoły naukowe) historii badań i nauczania matematyki, zostały podniesione. Druga część poświęcona jest pewnemu równaniu funkcjonalno-różniczkowemu, uogólniającemu równanie całkowo-różniczkowe badane przez J. Bodzionego, S. Gołąba i J. Szarskiego w związku z problemami technicznymi przy przesiewaniu materiałów sypkich.