The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let (Lv)(t)=∑i,j=1n(−1)jdj(s^2α(t)bij(t)μ(t)div(t)), be a non-selfadjoint differential operator on the Hilbert space L2(Ω) with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator L be sufficiently more general than [11] and [12] as defined in Section 1. In this paper, we estimate the resolvent of the operator L on the one-dimensional space L2(Ω) using some analytic methods.