Abstract:

By using Banach fixed point theorem in cone, one sufficient condition of the existence and uniqueness of a monotone decreasing positive solution was established to the nonlinear third-order two-point boundary value problem:u″+q(u′)f(t,u)=0, a.e. t∈［0,1］,u′(0)=A, u(1)=B, u″(0)=C,　where A≤0,　B≥0,　C≤0　were constants。

Key words: boundary value problem; fixedpoint theorem; monotone decreasing positive solution