On a boundary value problem with matrix coefficient which has spectral parameter in boundary conditi

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