Displaying similar documents to “Subdominant positive solutions of the discrete equation Δ u ( k + n ) = - p ( k ) u ( k ) .”

On the behavior of the solutions to autonomous linear difference equations with continuous variable

Christos G. Philos, Ioannis K. Purnaras (2007)

Archivum Mathematicum

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Autonomous linear neutral delay and, especially, (non-neutral) delay difference equations with continuous variable are considered, and some new results on the behavior of the solutions are established. The results are obtained by the use of appropriate positive roots of the corresponding characteristic equation.

Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms

George E. Chatzarakis, Ponnuraj Dinakar, Srinivasan Selvarangam, Ethiraju Thandapani (2022)

Mathematica Bohemica

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We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known...

One case of appearance of positive solutions of delayed discrete equations

Jaromír Baštinec, Josef Diblík (2003)

Applications of Mathematics

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When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation Δ u ( k + n ) = f ( k , u ( k ) , u ( k + 1 ) , ⋯ , u ( k + n ) ) is considered. Sufficient conditions concerning f are formulated in order to guarantee the existence of a positive solution for k → ∞ . An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results...

Oscillation of delay differential equations

J. Džurina (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.