Topics On The Distribution Eigenvalues Of Non-Selfadjoint Elliptic Systems Of Differential Operators

[[abstract]]In this paper, we first consider a non - selfadjoint differen-tial operator on Hilbert space Hℓ = L^2(0, 1)^ℓ with Dirichlet-type boundary conditions in form (The equation is abbreviated) Here, 0 ≤ β ＜ 1, t ∈ [0, 1] and the matrix function A(t) has distinct eigenvalues μ1(t), . . . , μℓ(t) which are different from zero and located in the complex plane in veiw of _φ, where _φ = {z ∈ C : |arg z| ＜ φ, φ ∈ (0, π)}. Finally, we investigate some spec-tral properties of the degenerate non-selfadjoint elliptic differential operators P acting on Hℓ. In particular, we will determine the resolvent estimate of the operator P that satisfies Dirichlet-type boundary conditions in spaces H_1 and Hℓ