Problem definition and some difficulties of its solution Consider a system of singularly perturbed differential equations (SPDE) εy'(x,ε)-A(x)y(x,ε) = h(x) (0.1) with ε → +0, x ∈ I= [0;l], where A(x) = (a_(ij)(x))~2_(i,j=1) is a known matrix, h(x) = colon (h_1(x),h_2(x)) is a given vector-function, and y(x,ε) = colon (y_1(x,ε),y_2(x,ε)) is the desired vector-function. The goal of this paper is to construct a uniform asymptotics of a solution (UAS) of system (0.1) which is suitable on the whole segment [0;L], provided this system has a turning point x = 0.
展开▼
