Extensions of Singular Fourth Order Dynamic Operators with Transmission Conditions

Source abstract

In the present paper, a singular fourth-order dynamic operator on time scales is investigated in the presence of impulsive conditions. Initially, a suitable boundary value framework adapted to the impulsive structure of the operator is constructed. Subsequently, the maximal dissipative, self-adjoint, and further appropriate extensions of the associated singular fourth-order differential operator, which acts on unbounded time scales under impulsive effects, are comprehensively characterized.