Second-Order Multiparameter Problems Containing Complex Potentials

In this work, we provide some lower bounds for the number of squarly integrable solutions of some second-order multiparameter differential equations. To obtain the results, we use both Sims and Sleeman’s ideas and the results are some generalization of the known results. To be more precise, we firstly construct the Weyl–Sims theory for the singular second-order differential equation with several spectral parameters. Then, we obtain some results for the several singular second-order differential equations with several spectral parameters

Spectral analysis of the direct sum Hamiltonian operators

In this paper we investigate the deciency indices theory and the selfad-joint and nonselfadjoint (dissipative, accumulative) extensions of the minimal symmetric direct sum Hamiltonian operators. In particular using the equivalence of the Lax-Phillips scattering matrix and the Sz.-Nagy-Foias characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces.Keywords: Hamiltonian system, dissipative operator, characteristic function, scattering matrix, completeness theore

Singular conformable sequential differential equations with distributional potentials

In this paper we consider the singular conformable sequential equation with distributional potentials. We present Weyl's theory in the frame of conformable derivatives. Moreover we give two theorems on limit-point case.Mathematics Subject Classification (2010): Primary 34B20; Secondary 26A33.Keywords: Weyl theory, Hilbert space, conformable equatio