Some singular singularly- perturbed problems(1)

摘要

In this paper, we study some singular singularly-perturbed boundary-value problem P_εconsisting of the differential equations formula(ell.) and the boundary conditions formula(ell.) where t∈[0,1], 0<ε≤ε_0. U, V, H_1 and H_2 are scalar functions and infinitely differential with respect to their variables respectively. our approach is somewhat similar to those of Chang[2], Shi[6]and Smith [7]. Our main result(Theorem 4)is new and extends the result, in the scalar case, of Shi[6], who dealt with the problem(1)with V(t, x,ε~2 y,ε)in place of V(t, x,εy,ε). An application of our result is given at the end.