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Dergiler / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 3

An expansion result for a Sturm-Liouville eigenvalue problem with impulse

Gusein Sh. GUSEINOV
Serife FAYDAOĞLU
Sayfa
355–366
Yayın Tarihi
2022-11-05
DOI
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The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The paper is concerned with an eigenvalue problem for second order differential equations with impulse.
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Temel Bulgular & Veri:Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite.
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Sonuç & Katkı:The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Green's function · Completely continuous operator · Impulse conditions

Özet

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

Abstract

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

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Bu Makaleye Atıf Yap

GUSEINOV, G. S., FAYDAOĞLU, S. (2022). An expansion result for a Sturm-Liouville eigenvalue problem with impulse. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 3, 355–366. https://ajindex.com/articles/608537

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Kaynakça (16)

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  16. Wang, A., Sun, J. and Gao, P.: Completeness of eigenfunctions of Sturm-Liouville problems with transmission conditions, J. Spectral Math. Appl., Vol. 2006, 10pp. (electronic). Serife FAYDAO ˘GLU Department of Engineering, Dokuz Eyl¨ul University, Buca, ˙Izmir-TURKEY e-mail: [email protected] Gusein Sh. GUSEINOV Department of Mathematics, Atilim University, ˙Incek, Ankara-TURKEY e-mail: [email protected]