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Integral Characteristic Function of a Nonlinear Sturm–Liouville Problem

Integral Characteristic Function of a Nonlinear Sturm–Liouville Problem We propose a new approach to the study of Sturm–Liouville problems nonlinear in thespectral parameter. The approach is based on the introduction of a transcendental functionrelated to the problem under study, called the integral characteristic function, which determinesthe eigenvalues of the Sturm–Liouville problem in question. The study of this function permitsone to prove the solvability of the problem, find the eigenvalue asymptotics, obtain comparisontheorems, and introduce a natural numbering of the eigenvalues and zeros of the eigenfunctions.We use this approach to study a nonlinear Sturm–Liouville problem on an interval with boundaryconditions of the first kind. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Integral Characteristic Function of a Nonlinear Sturm–Liouville Problem

Differential Equations , Volume 57 (12) – Dec 1, 2021

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References (29)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266121120016
Publisher site
See Article on Publisher Site

Abstract

We propose a new approach to the study of Sturm–Liouville problems nonlinear in thespectral parameter. The approach is based on the introduction of a transcendental functionrelated to the problem under study, called the integral characteristic function, which determinesthe eigenvalues of the Sturm–Liouville problem in question. The study of this function permitsone to prove the solvability of the problem, find the eigenvalue asymptotics, obtain comparisontheorems, and introduce a natural numbering of the eigenvalues and zeros of the eigenfunctions.We use this approach to study a nonlinear Sturm–Liouville problem on an interval with boundaryconditions of the first kind.

Journal

Differential EquationsSpringer Journals

Published: Dec 1, 2021

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