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Journals / Mühendislik Bilimleri Dergisi / 2002 / Cilt: 8 - Sayı: 2

Eigenfunctions of discontinuous sturm-liouville problem containing eigenvalue parameter in the one of boundary conditions

Sınır şartlarının birinde özdeğer parametresi bulunduran süreksiz Sturm- Liouville probleminin özfonksiyonları

Oktay MUHTAROV
MAHİR KADAKAL
Fahrettin Ş. MUHTAROV
Pages
219–226
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Further, the basic solutions $phi(x,lambda)$ and $chi(x,lambda)$ are defined by the special procedure.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper by using a new approach we investigate the resolvent operator and completeness of the system of eigenfunctions of the Sturm-Liouville problem with discontinuous coefficients and weight, one of the boundary conditions of which contained linear eigenparameter.
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Key Findings & Data:For operator-theoretic formulation of the considered problem we define a new equvalent inner product in the Hilbert space $L_2[a,b]bigoplusC$ and suitable selfadjoint linear operator in it.
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Conclusion & Impact:Further, the basic solutions $phi(x,lambda)$ and $chi(x,lambda)$ are defined by the special procedure.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper by using a new approach we investigate the resolvent operator and completeness of the system of eigenfunctions of the Sturm-Liouville problem with discontinuous coefficients and weight, one of the boundary conditions of which contained linear eigenparameter. For operator-theoretic formulation of the considered problem we define a new equvalent inner product in the Hilbert space $L_2[a,b]bigoplusC$ and suitable selfadjoint linear operator in it. Further, the basic solutions $phi(x,lambda)$ and $chi(x,lambda)$ are defined by the special procedure.

Özet

Bu çalışmada, sınır şartlarının birinin katsayıları özdeğer parametresini lineer olarak içeren süreksiz katsayılı ve ağırlıklı Sturm-Liouville probleminin rezolvent operatörü ve özfonksiyonlar sisteminin tamlık özellikleri yeni bir yaklaşımla incelenmiştir. İncelenen problemin operatör-teorik yazılımı için $L_2[a,b]bigoplusC$ Hilbert uzayında yeni eşdeğer iç çarpım ve uygun kendine eşlenik lineer operatör tanımlanmıştır. Ayrıca, $phi(x,lambda)$ ve $chi(x,lambda)$ temel çözümleri özel bir yöntemle tanımlanmıştır

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Cite This Article

MUHTAROV, O., KADAKAL, M., MUHTAROV, F. Ş. (2002). Eigenfunctions of discontinuous sturm-liouville problem containing eigenvalue parameter in the one of boundary conditions. Mühendislik Bilimleri Dergisi, Cilt: 8 - Sayı: 2, 219–226. https://ajindex.com/articles/289254

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References (8)

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