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A uniqueness and existence theorem for a singular third-order boundary value problem on \([0,\infty)\). (English) Zbl 1021.34020
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:
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B60 Applications of boundary value problems involving ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
76S05 Flows in porous media; filtration; seepage
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References:
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