Bounds for the spectrum of a matrix differential operator with a damping term (Q638645)

The paper deals with the spectral problem for the operator generated by the differential expression \[ -\frac{d^2}{dx^2} + 2B(x)\frac{d}{dx} + C(x) \] with \(n\times n\)-matrix coefficients \(B(x)\) and \(C(x)\) given on a finite interval, and self-adjoint boundary conditions at the ends of the interval. The main results are an estimate for the resolvent and bounds for the spectrum. This allows the author to study the stability problem and to provide stability and instability conditions. The method relies on establishing the similarity between the operator in question and an operator without damping term (the coefficient of the first derivative).