Time scale theory helps us to combine differential equations with difference equations. Especially in models such as biology, medicine, and economics, since the independent variable is handled discrete, it requires analyze discrete clusters. In these cases, defined $\mathbb{Z}$ are considered. Boundary value problems (BVP's) used solve model many physical areas. this study, we examined spectral...

From the point of view of differential geometry and mathematical physics, the Riemann zeta function appears as the operator zeta function associated to the Laplacian operator on the line segment [18] [17] [5] [6] [14]. A natural generalisation of this setting, is to consider a Sturm Liouville operator instead, i.e. a singularity at one of the end points [9] [10] [11] [7] [8][16]. This leads aga...

We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method...

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using operator-theoretical formulation, transfer the to operator in appropriate Hilbert space. It is proved that self-adjoint. We also give asymptotic formulas of eigenvalues problem. Moreover, Green’s function discussed.