Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions (Q1035054)

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 \(L\).