GREEN'S FUNCTION FOR NON-SELF-ADJOINT DIFFERENTIAL OPERATOR WITH BLOCK-TRIANGULAR OPERATOR COEFFICIENTS

In this paper for Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is obtained decreasing and increasing at infinity operator solutions. For them, the asymptotic behavior at infinity was found out. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For it, we constructed Greens function for the non-self-adjoint differential operator.