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Unbounded upper and lower solution method for third-order boundary-value problems on the half-line. (English) Zbl 1190.34026

The authors consider the nonlinear boundary value problem

u ''' (t)+a(t)f(t,u(t),u ' (t),u '' (t))=0,t(0,+),u(0)=u ' (0)=0,u '' (+)=0,(1)

where a:(0,+)(0,+), f:[0,+)× 3 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 A. I. Kolosov and S. V. Kolosova [On two-sided approximations in the solution of the Falkner-Skan problem. Mat. Fiz. 23, 63–67 (1978; Zbl 0447.34014)].

MSC:
34B40Boundary value problems for ODE on infinite intervals
34B15Nonlinear boundary value problems for ODE