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, ...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′ 2 i 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.展开更多
文摘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′ 2 i 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.
