具有不定权的非线性常微分方程的正周期解对：超次线性情形的拓扑度方法
Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case
摘要：
研究了二阶非线性微分方程\begin{equation*} u'' + c u' + λa(t) g(u) = 0, \end{equation*}的周期边值问题和Neumann边值问题，其中$g \colon \mathopen{[}0,+\infty\mathclose{[}\to \mathopen{[}0,+\infty\mathclose{[}$是在无穷远处具有超线性增长的次线性函数.当$\int_{0}^{T} a(t) \!dt < 0$和$λ> 0$充分大时，证明了两个正解的存在性.我们的方法是基于Mawhin的重合度理论和指数计算。
英文摘要：
We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation \begin{equation*} u'' + c u' + λa(t) g(u) = 0, \end{equation*} where $g \colon \mathopen{[}0,+\infty\mathclose{[}\to \mathopen{[}0,+\infty\mathclose{[}$ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when $\int_{0}^{T} a(t) \!dt < 0$ and $λ> 0$ is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
