TY - JOUR AU - Podowski, MichaƂ TI - ANALYSIS OF AN OPERATOR EQUATION WITH THE DIFFERENTIABLE IN BANACH SPACE OPERATOR AND ITS APPLICATION TO THE INVESTIGATION OF REACTOR MODEL DYNAMICS JF - Journal of Power Technologies; Vol 45 (1977) KW - N2 - An operator equation of the following form λx = z + F(x), where z - an element of Banach space X and F(x)∈X for x∈D⊂X, is investigated. In the cas of m-order differentiable operator F (m>3), conditions of existence and uniqueness of a solution of considered equation are formulated and an estimation of the norm of this solution as a function of the norm z is obtained. The results of theoretical analysis are applied to the point reactor model with nonlinear, temperature-type reactivity feedback. The conditions of the asymptotic stability for the autonomous system as well as for the system including the external reactivity oscilations, are formulated. UR - https://papers.itc.pw.edu.pl/index.php/JPT/article/view/117