Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions. (English) Zbl 1228.34136

Bairamov, Elgiz; Yokus, Nihal

Abstr. Appl. Anal. 2009, Article ID 289596, 8 p. (2009).

Summary: Let \(L\) denote the operator generated in \(L_2(\mathbb R_+)\) by the Sturm-Liouville problem
\[ -y''+q(x)y=\lambda^2y,\quad x\in\mathbb R_+=[0,\infty),\quad y'(0)/y(0)=\alpha_0+\alpha_1\lambda+\alpha_2\lambda^2, \]
where \(q\) is a complex-valued function and \(\alpha_i\in\mathbb C\), \(i=0,1,2\), with \(\alpha_2\neq 0\). We investigate the eigenvalues and the spectral singularities of \(L\) and obtain analogs of Naimark and Pavlov conditions for \(L\).

MSC:

34L05	General spectral theory of ordinary differential operators
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L15	Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34B24	Sturm-Liouville theory

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