Zdenek Smarda

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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)
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)
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)
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)
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)