ON A BOUNDARY VALUE PROBLEM WITH MATRIX COEFFICIENT WHICH HAS SPECTRAL PARAMETER IN BOUNDARY CONDITION

Abstract

In this paper following boundary value problem is considered. - y'' + Q(x) y = lambda R(x) y, a < x < b y' (x) = 0 beta(1)y(b) - beta(2)y'(b) = lambda alpha y(b) Here Q(x), R(x) is n x n self-adjoint matrix functions, R(x) is positive matrix, alpha, beta(1), beta(2) are constants satisfy some conditions and lambda is a spectral parameter. The spectrum of considered boundary value problem is investigated and the expansion formulas according to eigenvalues are obtained.