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Zbl 1190.34026
Bai, Chuanzhi; Li, Chunhong
Unbounded upper and lower solution method for third-order boundary-value problems on the half-line. (English)
[J] Electron. J. Differ. Equ. 2009, Paper No. 119, 12 p., electronic only (2009). ISSN 1072-6691/e

The authors consider the nonlinear boundary value problem $$\gathered u'''(t)+ a(t) f(t,u(t), u'(t), u''(t))= 0,\quad t\in (0,+\infty),\\ u(0)= u'(0)= 0,\quad u''(+\infty)= 0,\endgathered\tag1$$ where $a: (0,+\infty)\to (0,+\infty)$, $f: [0,+\infty)\times \bbfR^3\to \bbfR$ are continuous. By using the upper and lower solutions method, the authors present sufficient conditions for the existence of solutions to (1). Note: The authors point out that no other works on boundary value problems on the half-line for third-order differential equation by the other researchers have been considered by them as a prototyp. Such problem has been considered, for example, in the work of {\it A. I. Kolosov} and {\it S. V. Kolosova} [On two-sided approximations in the solution of the Falkner-Skan problem. Mat. Fiz. 23, 63--67 (1978; Zbl 0447.34014)].
[Anatolij Ivan Kolosov (Khar'kov)]

MSC 2000:: *34B40 Boundary value problems on infinite intervals
34B15 Nonlinear boundary value problems of ODE

Keywords: upper and lower solutions; third-order boundary-value problem; half-line; Nagumo-condition

Citations: Zbl 0447.34014

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