SINGULAR PERTURBATION PROBLEM FOR THE SYSTEM OF LINEAR INTEGRAL EQUATIONS

In the paper we use the boundary layer function method （cf,[1]） to consider the following problem;where y,f and z,g are m and r-dimensional vector value functions respectively; f,g are smooth enough on[0,1]×[O,ε0] for some ε0】0; kij;, i, j=1,2, with the corresponding order for the system are smoothenough on [0,1]×[0, 1] except for the line x=s and there are jumps:Jij（x） = Kij（x,x-） -Kij（x,x+）, x∈[0, 1],i,j = 1,2.At the first, we make the hypothesis as follows（I） J22（x）∈C（[0,1]）, and its all eigenvalues have nonzero real parts for x∈[0,1].By the condition we can take the kernel matrices and vector functions of （1） in following block forms: