Existence and uniqueness for nonlinear boundary value problems on infinite intervals

Baxley, John V.

doi:10.1016/0022-247x(90)90388-v

Cited by 85 publications

(45 citation statements)

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“…Boundary value problems on the half-line arise quite naturally in the study of radially symmetric solutions of nonlinear elliptic equations and there are many results in this area; see [1][2][3][4][5] for examples. On the other hand, the theory of impulsive differential equations has been emerging as an important area of investigations in recent years (see [14,15]).…”

Section: Introductionmentioning

confidence: 99%

Boundary Value Problems on the Half-Line with Impulses and Infinite Delay

Yan

2001

Journal of Mathematical Analysis and Applications

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Section: Introductionmentioning

confidence: 99%

Boundary Value Problems on the Half-Line with Impulses and Infinite Delay

Yan

2001

Journal of Mathematical Analysis and Applications

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“…For some previous related results, see [4,5,24]. By a combination of the methods applied in [2] with the ideas and techniques of this paper, one can extend the results in [2] to the more general case of the singular IVP (5.4), (1.2), (5.5).…”

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confidence: 94%

On a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems

Philos

2007

Ann. Polon. Math.

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Abstract. This article is concerned with a boundary value problem on the half-line for nonlinear two-dimensional delay differential systems. By the use of the SchauderTikhonov theorem, a result on the existence of solutions is obtained. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of solutions is established. Moreover, these results are applied to the special case of ordinary differential systems and to a certain class of delay differential systems. Furthermore, applications to differential systems of Emden-Fowler type and to linear differential systems are presented, and two specific examples are given.1. Introduction and statement of the main results. In the last few years, there is a great activity in studying the problem of the existence of solutions of boundary value problems on the half-line for second order nonlinear delay (and, in particular, ordinary) differential equations (see, for example, [7,23,25,26,30,36,37,39,40]). A closely related problem is that of the existence of solutions with prescribed asymptotic behavior for delay (and, especially, ordinary) differential equations. Among numerous articles dealing with this problem, we refer to [19,20,28,29,31,32] and the references cited therein.On the other hand, several articles have appeared in the literature, which are concerned with the asymptotic behavior of solutions of nonlinear ordinary differential systems. See, for example, [18,21,22,38]

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“…We remark at this point that almost all the literature [1,5,10 16] on singular problems is devoted to the case f (t, u, z)# f (t, u). Only very specific situations [2,3,9,10,13] have been examined in the more general situation (i.e. in the case f (t, y, py$)).…”

Section: Introductionmentioning

confidence: 99%