A Differential Boundary Operator of the Sturm–Liouville Type on a Semiaxis with Two-Point Integral Boundary Conditions

Abstract

We prove that a differential boundary operator of the Sturm–Liouville type on a semiaxis with two-point integral boundary conditions that acts in the Hilbert space L ₂(0, ∞) is closed and densely defined. The adjoint operator is constructed. We also establish criteria for the maximal dissipativity and maximal accretivity of this operator.