A boundary value problem on the half-line for higher-order nonlinear differential equations

Abstract

This article is devoted to the study of the existence of solutions as well as the existence and uniqueness of solutions to a boundary-value problem on the half-line for higher-order nonlinear ordinary differential equations. An existence result is obtained by the use of the Schauder-Tikhonov theorem. Furthermore, an existence and uniqueness criterion is established using the Banach contraction principle. These two results are applied, in particular, to the specific class of higher-order nonlinear ordinary differential equations of Emden-Fowler type and to the special case of higher-order linear ordinary differential equations, respectively. Moreover, some (general or specific) examples demonstrating the applicability of our results are given.

Solvability of boundary value problems for second order impulsive differential equations on whole line with a non-Carathédory nonlinearity

“…The theory of impulsive differential equation has recently received considerable attention, see [30,31,32]. However, the study on existence of positive solutions of nonlocal boundary value problems for impulsive differential equations on whole real line has not been sufficiently developed [2,3,5,4,8,9,26].…”