Periodic Solutions for a Class of Semilinear Euler-Bernoulli Beam Equations with Variable Coefficients

被引：0

作者：

Wei, Hui ^{[1
]}

Ji, Shuguan ^{[2
,3
]}

机构：

[1] Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China

[2] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[3] Northeast Normal Univ, Ctr Math & Interdisciplinary Sci, Changchun 130024, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2025年 / 37卷 / 01期

关键词：

Existence; Periodic solutions; Beam equation; DIMENSIONAL WAVE-EQUATION; VIBRATIONS; KAM;

D O I：

10.1007/s10884-023-10296-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of periodic solutions for a class of semilinear Euler-Bernoulli beam equations with variable coefficients. Such a mathematical model is used to describe the infinitesimal, free, undamped in-plane bending vibrations of a thin straight elastic beam. When the frequency is rational, we acquire some fundamental properties of the variable coefficients beam operator and in particular prove that its inverse operator is compact on its range. Based on these properties, we obtain the existence of periodic solutions when the nonlinear term is monotone and bounded.

引用

页码：237 / 249

页数：13

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