Ramazan Ozarslan

Sturm-Liouville Difference Equations Having Special Potentials

In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few applications are given to show the requirement of Sturm-Liouville difference equations having potential function in view of suitability to the spectral theory. The approximate numerical outcomes for the eigenfunctions are compared with each other.

Spectral results of Sturm-Liouville difference equation with Dirichlet boundary conditions

In this work, the boundary value problem for Sturm-Liouville difference equation, which has variable potential function q(n), with Dirichlet boundary conditions is considered. The sum representation of solution is obtained and by virtue of this result, asymptotic formula of the eigenfunction is given.

Re-establishment singular spectral problem by nodal data

In this study, we are concerned with singular Sturm-Liouville Problem by using a new kind of spectral data that is known as nodal points. We obtain some asymptotic results about the problem. Furthermore, we prove a re-establishment formula for singular potential.

Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations

In this study, Sturm-Liouville problem with variable coefficient, potential function q (n), for difference equation is considered. The representation of solutions is obtained by variation of parameters method for two different initial value problems and trigonometric solutions are found by means of complex characteristic roots. It is proved that these results hold the equation by using summation by parts method. Two estimations of asymptotic expansion of the solutions are established.