Singular Perturbations of Boundary Problem for a Vector Second Order Equation.

摘要

The author studies the boundary value problem epsilon(y double prime) + A(t,epsilon, y)y' = f(t,epsilon, y) y(0,epsilon) =alpha(epsilon), y(1,epsilon) =beta(epsilon),where epsilon > 0is a small parameter, y, f,alpha,beta are n-dimensional vector functions and A is an n x n matrix function. This vector boundary problem does not appear to have been studied,although the scalar boundary problem has been treated extensively. Under appropriate assumptions,the author obtains existence of solution as in the scalar problem. A converse result is also obtained. (Author)