GREEN'S FUNCTION FOR NON-SELF-ADJOINT DIFFERENTIAL OPERATOR WITH BLOCK-TRIANGULAR OPERATOR COEFFICIENTS
ALEKSANDR KHOLKIN *
Department of Higher and Applied Mathematics, Pryazovskii State Technical University, 7 Universitets’ka Street, 87500, Mariupol, Ukraine.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Differential operators, block-triangular operator coefficients, Greens function