Using the fixed point theorem in partially ordered sets, we obtain sufficient conditions for existence of a unique positive solution to boundary-value problem Sturm-Liouville type nonlinear ordinary differential equation, and give an example illustrating results obtained.

The purpose of this study is to examine the properties scattering solutions and function an impulsive Sturm-Liouville boundary value problem on semi axis. By using Jost solutions, we obtain function, asymptotic representation resolvent operator. Finally, unperturbated equation.

This paper is devoted to investigating the uniform convergence conditions of Fourier series expansions continuous functions in terms eigenfunctions a Sturm-Liouville problem with eigenparameter one boundary on closed interval. Such problems are quite common mathematical physics problems.

In this paper, we consider the inverse nodal problem for a quadratic pencil of Sturm$-$Liouville equations with parameter-dependent Bitsadze$-$Samarskii type nonlocal boundary condition and give an algorithm reconstruction potential functions by obtaining asymptotics points.

In this paper, a Sturm–Liouville problem with some nonlocal boundary conditions of the Bitsadze-Samarskii type is studied. We show that coefficients can be uniquely determined by dense set nodal points. Moreover, we give an algorithm for reconstruction potential function and other in conditions.