源于流体边界层理论的一类奇异非线性边值问题

Nonlinear Singular Boundary Value Problem Arising in Boundary Layer Theory of Fluids

利用奇异摄动法技巧,对源于流体边界层理论中的一类奇异非线性边界值问题(ρ(t)g′(t))′+q(t)f(t,g)+h(t)=0,0<t<1,g′(0)=c,g(1)=0进行了研究,其中f(t,g)在g=0处可以具有奇性。得到了问题正解的存在性和唯一性的充分条件。

The positive solutions of a class of sec ond-order nonlinear singular boundary value problem （p（t）g＇（t））＇＋q（t）f（t,g）＋h（t）=0,0〈t〈1,g＇（0）=c,g（1）=0 is studied, where f（ t ,g ） may be singular at g = 0. This problem is arising in the boandary layer theory. By utilizing the perturbation technique, sufficient conditions for the existence and uniqueness of positive solutions to the problems are obtained.