1-维次线性p-Laplacian方程的无穷多周期解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1462-1472.

1-维次线性p-Laplacian方程的无穷多周期解

王学蕾()

^{山东农业大学信息科学与工程学院山东泰安 271018}

收稿日期:2021-03-26 出版日期:2022-10-26 发布日期:2022-09-30
作者简介:王学蕾, E-mail: wangxl@sdau.edu.cn
基金资助:
国家自然科学基金(11671287);国家自然科学基金(61573228)

Large Multiple Periodic Solutions for the 1-Dimensional Sub-Linear p-Laplacian Equation

Xuelei Wang()

^{Department of Mathematics, College of Information Science and Engineering, Shandong Agricultural University, Shandong Taian 271018}

Received:2021-03-26 Online:2022-10-26 Published:2022-09-30
Supported by:
the NSFC(11671287);the NSFC(61573228)

摘要/Abstract

摘要：

该文研究1-维p-Laplacian方程$({\left|x'\right|}^{p-2} x')'+f(t, x)=0$end{document}周期解的存在性和多解性, 其中$f(t, x)$满足原点附近的次线性条件, 即$\lim\limits_{\mid x\mid \rightarrow 0} \frac{f(t, x)}{\mid x\mid^{p-2}x}= 0$.得到的存在性结果可以应用于经典方程$x''+f(t, x)=0$. 证明方法基于Poincaré-Birkhoff扭转定理.

关键词: Hamiltonian系统, 周期解, Poincaré-Birkhoff扭转定理, 盘旋性质

Abstract:

In this paper, we obtain existence and multiplicity of periodic solutions for 1-dimensional p-Laplacian equation $(|x'|^{p-2}x')'+f(t, x)=0$, where $f\in C(\mathbb{R} \times\mathbb{R} , \mathbb{R} )$ is \pi$-periodic in the first variable and satisfies the assumption $\frac{f(t, x)}{\mid x\mid^{p-2}x}\rightarrow 0$, as $\mid x\mid \rightarrow 0$. The new existence results can be applied to situations in which the more classical equation $x''+f(t, x)=0$. Proofs are based on Poincaré-Birkhoff twist theorem.

Key words: Hamiltonian systems, Periodic solution, Poincaré-Birkhoff twist theorem, Spiral property

中图分类号:

O175.14

王学蕾. 1-维次线性p-Laplacian方程的无穷多周期解[J]. 数学物理学报, 2022, 42(5): 1462-1472.

Xuelei Wang. Large Multiple Periodic Solutions for the 1-Dimensional Sub-Linear p-Laplacian Equation[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1462-1472.

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