#### Filter Results:

#### Publication Year

2007

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- 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)

- 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)

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.

- 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)

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)

- Zdeněk SMArdA
- 2012

ABSTrACT This paper proposed an efficient modification of homotopy perturbation transform method (HPTM), namely modified homotopy perturbation transform method (MHPTM) for the solution of third order boundary layer equation on semi-infinite domain. The technique was based on the application of Laplace transform to boundary layers in fluid mechanics. The… (More)