Abstract
This paper is concerned with the existence and uniqueness of solutions for the second-order nonlinear delay differential equations. By the use of the Schauder fixed point theorem, the existence of the solutions on the half-line is derived. Via the Banach contraction principle, another result concerning the existence and uniqueness of solutions on the half-line is established. The main results in this paper extend some of the existing literatures.
Highlights
Boundary value problems on unbounded interval have many applications in physical problems
Boundary value problems on unbounded interval concerning second-order delay differential equations are of specific interest in these applications
For second-order delay differential equations, boundary value problems on the halfline are closely related to the problems of existence of global solutions on the half-line with prescribed asymptotic behavior
Summary
Boundary value problems on unbounded interval have many applications in physical problems. Such problems arise, for example, in the study of linear elasticity, fluid flows, and foundation engineering see 1 and the references therein. Boundary value problems on unbounded interval concerning second-order delay differential equations are of specific interest in these applications. For second-order delay differential equations, boundary value problems on the halfline are closely related to the problems of existence of global solutions on the half-line with prescribed asymptotic behavior. There is, in particular, a growing interest in solutions of such boundary value problems see, e.g., 3. Concerning initial value problems, we refer to the monograph by Lakshmikantham and Leela 6 , while, regarding boundary value problems, we mention the monographs by Azbelev et al 7 and Azbelev and Rakhmatullina 8
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