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.

In this study, we find asymptotic estimates of eigenvalues for regular
 Sturm-Liouville problems having the eigenvalue parameter in all boundary
 conditions with symmetric single well potential that is to midpoint related interval and nonincreasing on first semi-region interval.

In Section 2, we give first an existence result for problems where the second, the functional argument u of g, is replaced in (1.1) by fixed functions v ∈ C(J), and study the dependence of solution sets of these problems on v. The so obtained results and a fixed point result for multifunctions proved recently in [7] are then used in Section 3 to derive existence results for minimal and maximal ...

This article concerns the existence and multiplicity of positive solutions for the singular Sturm-Liouville boundary value problem (p(t)u′(t))′ + h(t)f(t, u(t)) = 0, 0 < t <∞, au(0)− b lim t→0+ p(t)u′(t) = 0, c lim t→∞ u(t) + d lim t→∞ p(t)u′(t) = 0. We use fixed point index theory to establish our main results based on a priori estimates derived by utilizing spectral properties of associated l...

In this paper, the propagation and scattering of acoustic waves in a flexible wave-guide involving step discontinuity at an interface is considered. The emerging boundary value problem is non-Sturm-Liouville and is solved by employing a hybrid mode-matching technique. The physical scattering process and attenuation of duct modes versus frequency regime and change of height is studied. Moreover,...