2023
DOI: 10.32323/ujma.1216691
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On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and Negative Weight Function

Abstract: In this paper, we shall study the spectral properties of the non-selfadjoint operator in the space $L_{\varrho }^{2}\left(\mathbb{R}_{+}\right) $ generated by the Sturm-Liouville differential equation \begin{equation*} -y^{^{\prime \prime }}+q\left( x\right) y=\omega ^{2}\varrho \left( x\right) y, \quad x \in \mathbb{R}_{+} \end{equation*} with the integral type boundary condition \begin{equation*} \int \limits_{0}^{\infty }G\left( x \right) y\left( x\right) dx+ \gamma y^{\prime }\left( 0\right) -\theta y\left… Show more

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