Makin, Alexander Regularized trace of the Sturm-Liouville operator with irregular boundary conditions. (English) Zbl 1171.34355 Electron. J. Differ. Equ. 2009, Paper No. 27, 8 p. (2009). From the introduction: This paper deals with the eigenvalue problem for the Sturm-Liouville equation\[ u''-q(x)u+\lambda u=0 \tag{1} \]on the interval \((0,\pi)\) with the boundary conditions\[ u'(0)+ (-1)^\theta u'(\pi)+ bu(\pi)=0, \qquad u(0)+ (-1)^{\theta+1} u(\pi)=0, \tag{2} \]where \(b\) is a complex number, \(b\neq 0\), \(\theta=0,1\). The goal of this article is to calculate the first-order regularized trace for (1)–(2). Cited in 6 Documents MSC: 34L05 General spectral theory of ordinary differential operators 34B24 Sturm-Liouville theory Keywords:Sturm-Liouville operator; eigenvalue problem; spectrum PDFBibTeX XMLCite \textit{A. Makin}, Electron. J. Differ. Equ. 2009, Paper No. 27, 8 p. (2009; Zbl 1171.34355) Full Text: EuDML EMIS