SINIR �ARTLARININ B�R�NDE �ZDE�ER PARAMETRES�BULUNDURAN S�REKS�Z STURM-L�OUV�LLE PROBLEM�N�N �ZFONKS�YONLARI

MUHTAROV, Oktay; KADAKAL, Mahir; MUHTAROV, Fahrettin �.

Cilt : 8 Say� : 2 Y�l : 2024

30/2Son Say� Erken Bask� Ar�iv Pop�ler Makaleler Makale G�nderimi

Pamukkale �niversitesi M�hendislik Bilimleri Dergisi

SINIR �ARTLARININ B�R�NDE �ZDE�ER PARAMETRES�BULUNDURAN S�REKS�Z STURM-L�OUV�LLE PROBLEM�N�N �ZFONKS�YONLARI [Pamukkale Univ Muh Bilim Derg]

Pamukkale Univ Muh Bilim Derg. 2002; 8(2): 219-226

SINIR �ARTLARININ B�R�NDE �ZDE�ER PARAMETRES�BULUNDURAN S�REKS�Z STURM-L�OUV�LLE PROBLEM�N�N �ZFONKS�YONLARI

Oktay MUHTAROV¹, Mahir KADAKAL², Fahrettin �. MUHTAROV³
¹Gaziosmanpa�a �niversitesi, Fen-Edebiyat Fak�ltesi, Matematik B�l�m�, Tokat
²Ondokuz May�s �niversitesi, Fen-Edebiyat Fak�ltesi, Matematik B�l�m�, 55139-Kurupelit/Samsun
³Azerbaycan Bilimler Akademisi, Matematik ve Mekanik Enstit�s�, Bak�-Azerbeycan

Bu �al��mada, s�n�r �artlar�n�n birinin katsay�lar� �zde�er parametresini lineer olarak i�eren s�reksiz katsay�l� ve a��rl�kl� Sturm-Liouville probleminin rezolvent operat�r� ve �zfonksiyonlar sisteminin taml�k �zellikleri yeni bir yakla��mla incelenmi�tir. �ncelenen problemin operat�r-teorik yaz�l�m� i�in C L [a, b] 2 ? / Hilbert uzay�nda yeni e�de�er i� �arp�m ve uygun kendine e�lenik lineer operat�r tan�mlanm��t�r. Ayr�ca, ) ?(x,? ve ) ?(x,?) temel ��z�mleri �zel bir y�ntemle tan�mlanm��t�r.

Anahtar Kelimeler: S�reksiz Sturm-Liouville problemi, �zde�er, �zfonksiyon, Rezolvent operat�r

EIGENFUNCTIONS OF DISCONTINUOUS STURM-LIOUVILLE PROBLEM CONTAINING EIGENVALUE PARAMETER IN THE ONE OF BOUNDARY CONDITIONS

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 C L [a, b] 2 ? / and suitable selfadjoint linear operator in it. Further, the basic solutions ) ?(x,? and ) ?(x,?)are defined by the special procedure.

Keywords: Discontinuous Sturm-Liouville problem, Eigenvalue, Eigenfunctions, Resolvent operator

Oktay MUHTAROV, Mahir KADAKAL, Fahrettin �. MUHTAROV. EIGENFUNCTIONS OF DISCONTINUOUS STURM-LIOUVILLE PROBLEM CONTAINING EIGENVALUE PARAMETER IN THE ONE OF BOUNDARY CONDITIONS. Pamukkale Univ Muh Bilim Derg. 2002; 8(2): 219-226
Makale Dili: T�rk�e

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