Uniqueness of the Solution to the Inverse Problem of Scattering Theory for the Sturm-Liouville Operator System with a Spectral Parameter in the Boundary Condition

In this paper, we consider the boundary value problem (bvp) y(j)'' + lambda(2)y(j) = Sigma(n)(k=1) V-jk(x)y(k), x is an element of R+ := (0, infinity) y(j)'(0) + (alpha(0) + i alpha(1)lambda + alpha(2)lambda(2))y(j)(0) = 0, j = 1,2, ..., n) where lambda is the spectral parameter and V(x) = vertical bar vertical bar V-jk(x)vertical bar vertical bar(n)(1) is a Hermitian matrix such that sigma(1)(x) = integral(infinity)(x) t vertical bar V(t)vertical bar dx < infinity, x is an element of R+ and alpha(0), alpha(1) and alpha(2) are real numbers, alpha(1) <= 0, alpha(2) > 0, alpha(0) + i alpha(1)lambda + alpha(2)lambda(2) not equal 0 for lambda = i mu,mu > 0. We have obtained the uniqueness of the solution to the inverse problem of scattering theory on the semiaxis for the boundary value problem with a spectral parameter.