In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar...In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar functions and infinitely differentiable 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, ε2y, ε) in place of V(t, x, εy, ε). An application of our result is given at the end.展开更多
文摘In this paper, we study some singular singularly-perturbed boundary-value problem Pε consisting of the differential equations and the boundary conditions where t ∈ [0, 1], 0 <ε ≤ ε0. U, V, H1 and H2 are scalar functions and infinitely differentiable 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, ε2y, ε) in place of V(t, x, εy, ε). An application of our result is given at the end.
