Zdenek Smarda

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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.
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)