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- S. Stević, J. Diblik, B. Iričanin, Z. Šmarda
- 2014

AND APPLIED ANALYSIS, Vol. 2012, No. Article ID 54176, pp. 1-11, Nov, 2012 References: Abstract: Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.

- Stevo Stevic, Josef Diblík, Bratislav Iricanin, Zdenek Smarda
- Applied Mathematics and Computation
- 2015

- Josef Rebenda, Zdenek Smarda
- Applied Mathematics and Computation
- 2013

- Josef Diblı́k, Denys Ya. Khusainov, Irina V. Grytsay, Zdenĕk Šmarda
- 2010

1 Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic 2 Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveřı́ 331/95, 60200 Brno, Czech Republic 3 Department of Complex System Modeling,… (More)

- Zdeněk Šmarda
- 2010

The singular Cauchy problem for first-order differential and integro-differential equations resolved or unresolved with respect to the derivatives of unknowns is fairly well studied see, e.g., 1–16 , but the asymptotic properties of the solutions of such equations are only partially understood. Although the singular Cauchy problems were widely considered by… (More)

- J. Baštinec, J. Diblı́k, Z. Šmarda, Leonid Berezansky
- 2010

The existence of a positive solution of difference equations is often encountered when analysing mathematical models describing various processes. This is a motivation for an intensive study of the conditions for the existence of positive solutions of discrete or continuous equations. Such analysis is related to an investigation of the case of all solutions… (More)

- Leonid Berezansky, Josef Diblı́k, Zdenĕk Šmarda
- 2009

- Jaromı́r Baštinec, Leonid Berezansky, Josef Diblı́k, Zdeněk Šmarda, Allan C. Peterson
- 2010

and Applied Analysis 3 Theorem 1.3 see 7 . Let one assume that t − τ t ≥ t0 − τ t0 if t ≥ t0 and a t ≤ 1 τ t exp [ − ∫ t t−τ t 1 τ ξ dξ ] 1.10 as t → ∞. Then there exists an eventually positive solution x of 1.6 . In this paper we obtain new nonoscillation and oscillation sufficient conditions for 1.6 in the critical case, independent of Theorems 1.1−1.3.… (More)

A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competence of our method. Finally, two numerical examples arising in the theory of the radiative transfer, neutron transport and in the kinetic theory of… (More)

- Leonid Berezansky, Josef Diblík, Zdenek Smarda
- Computers & Mathematics with Applications
- 2010

In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t)+ a(t)ẋ(t)+ b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t)+ ∫ t t0 e ∫ t s a(ξ)dξb(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived. © 2010 Elsevier… (More)