A nodal inverse problem for second order Sturm–Liouville operators with indefinite weights

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.…”

Inverse Nodal Problems for the Sturm-Liouville Operator with Some Nonlocal Integral Conditions

“…In 2015, Juan P. Pinasco and Cristian Scarola studied an inverse problem for weighted Sturm-Liouville operators. By using weaker hypotheses for positive weights, the weight and the parameters were determined by a dense nodal set [15]. In 2018, Guangsheng Wei and Yongxia Guo provided the sharp conditions of the uniqueness for inverse nodal Sturm-Liouville problems.…”

Energy dependent potential problems for the one dimensionalp-Laplacian operator

“…This method works well also in the determination of the weight r, and different approaches were proposed in [31], based in the problem of moments combined with integration rules on the zeros of the eigenfunctions; in [25], where the authors used the WKB method; and recently in [29,30], based on the convergence of a sequence of measures concentrated on the zeros of the eigenfunctions.…”