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Zbl 1021.34020
Jiang, Daqing; Agarwal, R.P.
A uniqueness and existence theorem for a singular third-order boundary value problem on $[0,\infty)$. (English)
[J] Appl. Math. Lett. 15, No.4, 445-451 (2002). ISSN 0893-9659

Summary: It is proved that the singular third-order boundary value problem $$y'''=f(y),\quad y(0) = 0,\quad y(+\infty) = 1,\quad y'(+\infty) = y''(+\infty) = 0,$$ has a unique solution. Here, $f(y) = (1-y)^{\lambda}g(y)$, $\lambda > 0$, $g(y)$ is positive and continuous on $(0,1]$. The problem arises in the study of draining and coating flows.

MSC 2000:: *34B40 Boundary value problems on infinite intervals
34B16 Singular nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34B60 Applications of theory of BVP
34B18 Positive solutions of nonlinear boundary value problems
76S05 Flows in porous media

Keywords: singular third-order boundary value problem; singular nonlinear second-order initial value problem; positive solution; uniqueness; existence

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Zentralblatt MATH Berlin [Germany]