A general formalism is presented for the solution of boundary value problems arising in the description of transport of mass or energy through multiphase media, which consists in identifying physical conditions of interfaces with criteria for self-adjointness of the operators concerned. Several examples have been presented which demonstrate the advantages of the formalism.

In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of solution problem. study some spectral properties self-adjointness boundary-value Later, construct Green function for Finally, eigenfunction expansion is obtained.

Positivity, essential self-adjointness, and spectral properties of a class of Schrödinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established.

We give a sufficient condition for the essential self-adjointness of perturbation square magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function not necessarily bounded. allows perturbations that are bounded from below by constant.