摘要
具有非线性耗散项的拟线性波动方程的周期解问题,是一个困难问题.我们利用有限维投影法,在一定条件下,证明了带非线性耗散项的一维拟线性波动方程各种边值问题广义周期解存在,从而扩展了以往半线性方程的结果.
we consider BVP of quasilinear wave equations with nonlinear dissipation termwhere b,c and f are the time-periodic functions, aj,βi≥0,ai+β>0 j=1, 2. we assume that a, b, c and f satisfy the following condition: a(u)∈C2 (R1) and a'(w)>0, b∈C0, b(. ,ξ) is a strictly increasing function for ξ, and ξb≥r1 ξ p+1,b≤d1 ξ p+d2,c∈c0 and c≤dξ + e, f∈Lp+1(G). we have the following result: If the condition(2) holds, then the problem(1) has a periodic solution u∈D.
出处
《四川大学学报(自然科学版)》
CAS
CSCD
1992年第2期163-169,共7页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金资助项目
关键词
波动方程
拟线性
周期解
耗散项
periodic solution, nonlinear dissipation term, finite dimensional projection method.