New Type of Sturm-Liouville Problems in Associated Hilbert Spaces

الملخص EN

We introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation.

By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to spectral parameter.

Then we find sufficient conditions for discreteness of the spectrum and examine asymptotic behaviour of eigenvalues.

Obtained results are new even for continuous case, that is, without transmission conditions.