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- Zdeněk Šmarda
- 2007

In recent years the monotone iterative technique coupled with lower and upper solutions has been employed to obtain the existence of extremal solutions (which are limits of monotone sequences) for nonlinear ordinary differential equations, integral and integro-differential equations (see [1-6]). In this paper we determine conditions of the existence of… (More)

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

- Zdeněk Šmarda
- 2010

The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: gty t ayt1 ft, yt, t 0 Kt, s, yt, ysds, y0 0, t ∈ 0, t 0 , where a > 0 is a constant and t 0 > 0. An approach which combines topological method of T. Wa ˙ zewski and Schauder's fixed point theorem is used.

- S. Stević, J. Diblík, B. Iričanin, Z. Šmarda
- 2016

We show that the following system of difference equations x(n) = x(n-k)y(n-l)/(b(n)x(n-k) + a(n)y(n-l-k)); y(n) = y(n-k)x(n-l)/(d(n)y(n-k) + c(n)x(n-l-k)); n e No; where k, l e N, x(-i), y(-i) e R\{0}, i = 1; k+l, and sequences (a(n))neNo , (b(n))neNo , (c(n))neNo and (d(n))neNo are real, can be solved in closed form. For the case when the sequences a(n),… (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¨x(t) + a(t)˙ x(t) + b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ˙ y(t) + t t 0 e − t s a(ξ)dξ b(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived.

- S. Stević, J. Diblik, B. Iričanin, Z. Šmarda
- 2016

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.

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

- Josef Diblík, Zdenek Svoboda, Zdenek Smarda
- Computers & Mathematics with Applications
- 2008

- Jaromı́r Baštinec, Josef Diblı́k, Zdeněk Šmarda, Donal O’Regan
- 2009

A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Wa ˙ zewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem having the graph in a prescribed domain is proved.

- S. Stević, B. Iričanin, Z. Šmarda
- 2016

Closed form formulas of the solutions to the following system of difference equations: x(n) = (y(n–1)y(n–2))/(x(n–1)(a(n) + b(n)y(n–1)y(n–2)), y(n) = (x(n–1)x(n–2))/(y(n–1)(α(n) + β(n)x(n–1)x(n–2)), n No, where a(n), b(n), α(n), β(n), n No, and initial values x(–i), y(–i), i {1, 2}, are real numbers, are found. The domain of undefinable solutions to the… (More)