On the Existence of Nonlinearizable Solutions of a Nonclassical Two-Parameter Nonlinear Boundary Value Problem

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-07-30 DOI:10.1134/s0012266124040049

V. Yu. Martynova

引用次数: 0

Abstract

A nonlinear eigenvalue problem for a system of three equations with boundary conditions of the first kind, describing the propagation of electromagnetic waves in a plane nonlinear waveguide, is considered. This is a two-parameter problem with one spectral parameter and a second parameter arising from an additional condition. This condition connects the integration constants that arise when finding the first integrals of the system. The existence of nonlinearizable solutions of the problem is proved.

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论非经典双参数非线性边界问题的可非线性化解的存在性

摘要研究了描述电磁波在平面非线性波导中传播的具有第一类边界条件的三方程系统的非线性特征值问题。这是一个双参数问题，有一个频谱参数和一个附加条件产生的第二个参数。这个条件连接了在求系统的第一次积分时产生的积分常数。证明了该问题非线性可解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.