On the solvability of the Sturm – Liouville problem, nonlinear in the spectral parameter 

Gordey V. Chalyshov, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia) E-mail: 19gordey99@gmail.com

Background. The paper studies the solvability of the Sturm-Liouville problem, which is nonlinear in the spectral parameter. The problem is studied on a segment with boundary conditions of the third kind. Materials and methods. The main method for studying a problem is its equivalent reduction to an integral equation. Materials and methods. The main method for studying a problem is its equivalent reduction to an integral equation. Results. A theorem on the solvability of the integral characteristic equation is obtained and proven, which leads to the result on the solvability of the original problem; an additional condition is given that contains a restriction on the functions P and Q and allows one to obtain more meaningful results on solvability. Conclusions. The developed mathematical ap-paratus, namely the integral characteristic equation, will make it possible in the future to obtain results on the properties of eigenfunctions and eigenvalues, as well as their asymptotics.

Sturm–Liouville problem, integral characteristic function, solvability theorem, integral characteristic equation

Chalyshov G.V. On the solvability of the Sturm – Liouville problem, nonlinear in the spectral parameter. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;(4):105–117. (In Russ.). doi: 10.21685/2072-3040-2024-4-9