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Dergiler / Journal of New Results in Science / 2023 / Cilt: 12 Sayı: 1

Non-classical periodic boundary value problems with impulsive conditions

Sevda Nur ÖZTÜRK
Oktay MUKHTAROV
Kadriye AYDEMİR
Sayfa
1–8
Yayın Tarihi
2023-04-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem.
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Temel Bulgular & Veri: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.).
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Sonuç & Katkı:The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Non-classical periodic boundary value problems · Eigenvalues · Eigenfunctions

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.

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Bu Makaleye Atıf Yap

ÖZTÜRK, S. N., MUKHTAROV, O., AYDEMİR, K. (2023). Non-classical periodic boundary value problems with impulsive conditions. Journal of New Results in Science, Cilt: 12 Sayı: 1, 1–8. https://ajindex.com/articles/908087

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Kaynakça (16)

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