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Oscillatory properties of solutions of the fourth order difference equations with quasidifferences

Jankowski R., Schmeidel E., Zonenberg J.

Opuscula Mathematica

2014

Vol. 34, no. 4

789--797

A class of fourth-order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four-dimensional difference system. The sufficient conditions under which the considered equation has no quickly oscillatory solutions are given. Finally, the sufficient conditions under which the equation is almost oscillatory are presented.

Of neutral type hyperbolic integrodifferential equation

Pachpatte B. G.

Fasciculi Mathematici

2008

Nr 40

57-69

In this paper we study the existence, uniqueness and other properties of solutions of a certain neutral type hyperbolic integrodifferential equation in two independent variables. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.

Polynomial quasisolutions of linear differential-difference equations

Cherepennikov V. B., Ermolaeva P. G.

Opuscula Mathematica

2006

Vol. 26, no. 3

431-443

The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment t = 0 the value of the desired function x(t) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree N is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual Δ(t) = O(tN), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.

Oscillation for systems of neutral partial differential equations with continuous distributed deviating arguments

Li W. N., Meng F. W.

Demonstratio Mathematica

2001

Vol. 34, nr 3

619--633

Sufficient conditions are established for the oscillation of systems of neutral partial differential equations with continuous distributed deviating arguments. These results are illustrated by some examples.