Inverse problem for a quadratic pencil of Sturm–Liouville operator

Abstract

The purpose of this paper is to solve the inverse problem for a quadratic pencil of SturmLiouville operator on a finite interval. By using the Hochstadt's method, it is shown that the potential function can be given from two spectras as uniquely. Later, by generalizing this result, the Hochstadt's theorem which is related to the structure of difference for the potential functions is obtained.

Sınır Koşulunda Öz Parametre Bulunduran Bir Sturm-Liouville Operatörü İçin Ters Nodal Problem

“…Daha sonra, bazı yazarlar tarafından dikkate değer bazı sonuçlar elde edilmiştir. Örneğin, bazı yazarlar çalışmalarında nodal noktalar yardımıyla potansiyel fonksiyonu ve türevlerini yeniden yapılandırmıştır (Chen vd., 2002;Koyunbakan ve Panakhov, 2007;Koyunbakan ve Yılmaz, 2008;Koyunbakan, 2009Koyunbakan, , 2011Yang, 2014;Pinasco ve Scarola, 2015). Bu çalışmalara ek olarak bazı yazarlar sınır koşullarının öz parametreye bağlı olması durumunda ters nodal problemi ele aldılar (Browne ve Sleeman, 1996;Yılmaz ve Koyunbakan, 2010;Panakhov vd., 2010;Keskin ve Özkan, 2017;Şen, 2017, 2018.…”

Impulsive Diffusion Equation on Time Scales

“…Then, Gasymov and Guseinov [24] determined the diffusion operator from spectral data in 1981. Fragela [25] authors (see [33][34][35][36][37][38][39][40][41][42]). …”

Inverse problems for Sturm-Liouville difference equations

“…In the theory of inverse problems, it is assumed that certain spectral data are known, and the problem is to find the potential. This theory is well developed in the continuous case, and we refer to [3,4,6,8,[10][11][12] for further reading. It is well known [9, Chapter 0] that the problem (1)-(2) has infinitely many simple real eigenvalues λ 1 < λ 2 < .…”