Spectral Properties of the Sturm-Liouville Operator Produced by the Unseparated Boundary Conditions with Spectral Parameter

Abstract

In this study, firstly, the basic properties of the spectrum of the investigated problem were learned, sine and cosine type solutions were defined, their behaviors were examined and the properties of the solution of the given problem were learned with their help. Next, the characteristic equation of the studied problem was formed with the help of sine and cosine type solutions. Using the characteristic equation, the asymptotic behavior of the eigenvalues of the given problem and the ordering of the eigenvalues of the boundary value problems $L(\alpha _{j}),$ $j=1,$ $2$ when $\alpha_{1} $ $