Non-classical periodic boundary value problems with impulsive conditions

This study investigates some spectral properties of a new type periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that differential equation is given on two disjoint segments have common end, and additional interaction conditions are imposed this end (such called various names, including transmission conditions, jump interface impulsive etc.). At first, we proved all eigenvalues real there corresponding real-valued eigenfunction for each eigenvalue. Then showed eigenfunctions to different orthogonal. We also defined left right-hand solutions, terms which constructed transfer characteristic function. Finally, asymptotic formulas functions eigenvalues. results obtained generalization similar theory.