| Abstract: | We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), −1<t<1, Y(−1,ε)=A (ε), Y(1,ε)=B (ε). Supoosing some or all of the components of F, that is, f
i
satisfy ∂
2
f/∂ y’
i
2
|t=0=0, we say that F possesses a generalized turning point at t=0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior
of the solution when F possesses a generalized turning point at t=0. We mainly discuss regular-singular crossings. |
