Open Access Open Access  Restricted Access Subscription or Fee Access

Green’s Function for Finitely Many-Interval Sturm-Liouville Problem

Abdullah Kablan, Rodgers Chisha, Shady Haj Hasan

Abstract



The Green’s function has been constructed for one-interval and two-interval Sturm-Liouville problems in which the discontinuity of its derivative is not determined beforehand but occurs on its own. This paper seeks to extend that idea and construct the Green’s function for finitely many intervals case. We consider the second order scalar differential equation with its boundary conditions and convert it to its equivalent first order linear system. From this conversion, we formulate the characteristic function whose zeros are the eigenvalues of the homogeneous system. In addition, we construct the generalized matrix Green’s function from which we get the top right component as the Green’s function for finitely-many interval
Sturm-Liouville problem.

Keywords


Green’s function, Sturm-Liouville problem, characteristic function.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.