Non-classical periodic boundary value problems with impulsive conditions

Sevda Nur Öztürk; Oktay Mukhtarov; Kadriye Aydemir

Article Details

Non-classical periodic boundary value problems with impulsive conditions

Authors:

Sevda Nur Öztürk | Oktay Mukhtarov | Kadriye Aydemir

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Mathematical Sciences

Journal:

Journal of New Results in Science Vol.12 Issue 1, pp.1-8

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001289048

pISSN:

1304-7981

Keywords:

Abstract:

 This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.. At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

 This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.. At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

 This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.. At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

 This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.. At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

Article Details

Non-classical periodic boundary value problems with impulsive conditions

Authors:

Sevda Nur Öztürk | Oktay Mukhtarov | Kadriye Aydemir

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Mathematical Sciences

Journal:

Journal of New Results in Science Vol.12 Issue 1, pp.1-8

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001289048

pISSN:

1304-7981

Non-classical periodic boundary value problems

Eigenvalues

Eigenfunctions

Impulsive conditions

Issues

Article Details

Non-classical periodic boundary value problems with impulsive conditions

Authors: Sevda Nur Öztürk | Oktay Mukhtarov | Kadriye Aydemir

Publisher: Tokat Gaziosmanpasa University

Main Topics: Mathematical Sciences

Journal: Journal of New Results in Science Vol.12 Issue 1, pp.1-8

Document Type: Article

Publication Date: 4/2023

Document Language: English

Document ID (Org No.): 2001289048

pISSN: 1304-7981

Non-classical periodic boundary value problems

Eigenvalues

Eigenfunctions

Impulsive conditions

Issues

Authors:

Sevda Nur Öztürk | Oktay Mukhtarov | Kadriye Aydemir

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Mathematical Sciences

Journal:

Journal of New Results in Science Vol.12 Issue 1, pp.1-8

Document Type:

Article

Publication Date:

4/2023

Document Language:

English

Document ID (Org No.):

2001289048

pISSN:

1304-7981