Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

Abstract

We consider the operator $L$ generated in $L^2\left({?}_{+}\right)$ by the differential expression $l\left(y\right)=-y^{?}+q\left(x\right)y$, $x\in {?}_{+}:=[0,\infty )$ and the boundary condition $y^{\prime }\left(0\right)/y\left(0\right)={\alpha }_0+{\alpha }_1\lambda +{\alpha }_2{\lambda }^2$, where $q$ is a complex-valued function and ${\alpha }_i\in ?$, $i=0,1,2$ with ${\alpha }_2\ne 0$. In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of $L$.