西北师范大学学报（自然科学版）2026，Vol.62Issue(1)：72-76,92,6.DOI:10.16783/j.cnki.nwnuz.2026.01.009
Hilbert空间弱阻尼波方程周期解的存在唯一性
Existence and uniqueness of periodic solutions for weakly damped wave equations in Hilbert spaces
摘要
Abstract
The existence and uniqueness of periodic solutions for weakly damped wave equation u″(t)+2cu'(t)+Au(t)=f(t,u(t)),t∈R are discussed in a Hilbert space H,where A:D(A)⊂H →H is a positive definite self-adjoint operator with a compact resolvent in H,f:R×H →H is continuous,f(t,x)is ω-periodic in t,and c>0 is the damping coefficient.By applying the semigroup theory of linear operators and fixed-point theorem,the existence and uniqueness of ω-periodic solution of the equations are obtained.关键词
Hilbert空间/弱阻尼波方程/阻尼系数/周期解/算子半群/存在唯一性Key words
Hilbert space/weakly damped wave equation/damping coefficient/periodic solution/operator semigroup/existence and uniqueness分类
数理科学引用本文复制引用
高芸,李永祥..Hilbert空间弱阻尼波方程周期解的存在唯一性[J].西北师范大学学报（自然科学版）,2026,62(1):72-76,92,6.基金项目
国家自然科学基金资助项目(12061062) （12061062）
