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Kneser-type oscillation criteria for second-order half-linear advanced difference equations

Indrajith N., Graef John R., Thandapani E.

Opuscula Mathematica

2022

Vol. 42, no. 1

55--64

The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.

Stabilność abstrakcyjnych równań różniczkowych z wyprzedzonym argumentem

Jama D.

Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska

2010

z. 92

121-127

W artykule badane są, jakościowe własnosci pewnych rozwiązań abstrakcyjnych słabo nieliniowych równan różniczkowych z wyprzedzonym argumentem. Dowodzi się, stabilności rozwiązań w sensie Mowczana.

This paper treats the differential equation with the accelerated argument. This is the weak solution of the equation stable in the Mowczan's sense

On extremal solutions of differential equations with advanced argument

Augustynowicz A., Jankowski J.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

17-24

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.

On some generalized Volterra condition and advanced argument for integral equations

Augustynowicz A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2000

[Z] 40

7-17

We study the existence and uniqueness problem for wide class of nonlinear integral functional equations with an unknown function of several variables. We assume that the right-hand side of the equation satisfies some generalization of the Volterra condition that, in some cases, admits an advanced argument at an unknown function. The result is illustrated for some Darboux problem.

Oscillation of the solutions of nonlinear impulsive differential equations of the first order with advanced argument

Bainov D. D., Dimitrova M. B., Dishliev A. B.

Journal of Applied Analysis

1999

Vol. 5, nr 2

261-275

Sufficient conditions for oscillation of all solutions of a class of nonlinear impulsive differential equations of the first order with advanced argument and fixed moments of impulse effect are found.