Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term

Pub Date : 2023-10-05 DOI:10.58997/ejde.2023.65

Jiri Sremr

引用次数: 0

Abstract

We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{\lambda}\operatorname{sgn} u+\mu f(t);\quad u(0)=u(\omega),\; u'(0)=u'(\omega), $$ where $\mu\in \mathbb{R}$ is a parameter. We assume that $p,h,f\in L([0,\omega])$, $\lambda>1$, and the function $h$ is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term $f$ to change its sign. For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html

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具有变符号强迫项的非自治Duffing方程的参数相关周期问题

研究了以$\mu\in \mathbb{R}$为参数的周期问题$$ u''=p(t)u+h(t)|u|^{\lambda}\operatorname{sgn} u+\mu f(t);\quad u(0)=u(\omega),\; u'(0)=u'(\omega), $$的正解集的存在性、精确多重性和结构。我们假设$p,h,f\in L([0,\omega])$$\lambda>1$，函数$h$是非负的。所得结果扩展了现有文献中的已知结果。我们不要求相应线性问题的格林函数为正，并允许强迫项$f$改变其符号。＆＃x0D;欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html

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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