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A nonstandard Volterra integral equation on time scales

Reinfelds Andrejs, Christian Shraddha

Demonstratio Mathematica

2019

Vol. 52, nr 1

503--510

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

Asymptotic behavior of solutions of discrete Volterra equations

Migda J, Migda M.

Opuscula Mathematica

2016

Vol. 36, no. 2

265--278

We consider the nonlinear discrete Volterra equations of non-convolution type [formula] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(ns), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.

Comparison of properties of solutions of differential equations and recurrence equations with the same characteristic equation (on example of third order linear equations with constant coefficients)

Mikołajski J., Schmeidel E.

Opuscula Mathematica

2006

Vol. 26, no. 2

343-349

Third order linear homogeneous differential and recurrence equations with constant coefficients are considered. We take the both equations with the same characteristic equation. We show that these equations (differential and recurrence) can have solutions with different properties concerning oscillation and boundedness. Especially the numbers of suitable types of solutions taken out from fundamental sets are presented. We give conditions under which the asymptotic properties considered are the same for the both equations.

On the bounds for mean-values of solutions to certain third-order non-linear differential equations

Afuwape A. U., Adesina O. A.

Fasciculi Mathematici

2005

Nr 36

5-14

In this paper, the issue of bounds for the mean-values of solutions of some third-order differential equations with non-linear terms is considered. It is shown that these bounds are independent of the solutions for the considered equations.

Bounded oscillation for a class of even order neutral difference equations

Lin X., Shen J.

Fasciculi Mathematici

2002

Nr 33

37-47

We investigate bounded oscillation for the even order neutral delay difference equation delta'' (x(n) -cx(n-m) = pn(x-k), where u is even. The sufficient conditions obtained in this paper improve and generalize the results in related literature.