Stability estimates in nonlinear differential equations of a special kind

Quite a lot of works have been devoted to problems of stability theory and, in particular, to the use of the second Lyapunov method for this. The main ones are the following [1-7]. The main attention in these works is paid to obtaining stability conditions. At the same time, when solving practical problems, it is important to obtain quantitative characteristics of the convergence of solutions to an equilibrium position. In this paper, we consider nonlinear scalar differential equations with nonlinearity of a special form (weakly nonlinear equations). Differential equations of this type are encountered in the study of processes in neurodynamics [8,9]. In this paper, we obtain stability conditions for a stationary solution of scalar equations of this type. And also the characteristics of the convergence of the process are calculated. It is shown that the solution of stability problems is closely related to optimization problems [10-12]. Pages of the article in the issue: 67 - 71 Language of the article: Ukrainia

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

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Health and Skill Formation in Early Childhood

This paper analyzes the developmental origins and the evolution of health, cognitive, and socio-emotional skills during early childhood, from age 0 to 5. We explicitly model the dynamic interactions of health with the child’s behavior and cognitive skills, as well as the role of parental investment. A dynamic factor model corrects for the presence of measurement error in the proxy for the latent traits. Using data from the Avon Longitudinal Study of Parents and Children (ALSPAC), we find that children’s capabilities strongly interact and build on each other: health is an important determinant of early socio-emotional development; in turn socio-emotional skills have a positive impact on the evolution of both health and cognitive functions; on the other side, the effect of cognitive abilities on health is negligible. Furthermore, all facets of human capital display a high degree of persistence. Finally, mother’s investments are an important determinant of the child’s health, cognitive, and socio-emotional development early in life