可去奇点处波动方程中的Hopf-like分岔
Hopf-Like Bifurcation in a Wave Equation at a Removable Singularity
AI总结：
本文研究了一维阻尼波动方程在可去奇点处的Hopf-like分岔，通过消除线性化算子的奇异性，仅用压缩映射原理证明了小振幅周期解的存在。
摘要：
本文证明，当分岔参数为线性阻尼系数且为正并趋于零时，具有奇时间导数非线性的有阻尼一维波动方程表现出小振幅分岔的时间周期解。关键在于，临界状态下线性化算子的奇异性源于波动算子众所周知的小除数问题，而该奇异性被完全消除，无需通过Diophantine条件排除参数，也无需使用加速收敛方案。仅使用压缩映射原理即可。
英文摘要：
It is shown that a one-dimensional damped wave equation with an odd time derivative nonlinearity exhibits small amplitude bifurcating time periodic solutions, when the bifurcation parameter is the linear damping coefficient is positive and accumulates to zero. The upshot is that the singularity of the linearized operator at criticality which stems from the well known small divisor problem for the wave operator, is entirely removed without the need to exclude parameters via Diophantine conditions, nor the use of accelerated convergence schemes. Only the contraction mapping principle is used.
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。
