拟周期驱动Boussinesq方程响应解的存在性OA

In this paper,the existence of response solutions of the following Boussinesq equation with quasi-periodic force term and hinged boundary condition is considered,{ytt(t,x)=μyxxxxx+yxx+(y3)xx+εf(ωt,x),x∈T͂=[0,π],y(t,0)=y(t,π)=yxx(t,0)=yxx(t,π)=0,where μ>1,f:Td×T͂→R,Td=(R\2πZ)d is quasi-periodic with respect to t,d≥2 is a natural number,ω=(ω1,ω2,…,ωd)∈Rd\{0}is rationally independent,ε is sufficiently small,For both analytic and highly differentiable force terms,the corresponding existences of response solutions of the equation are obtained.In comparison with the known results,we extend the two-dimensional frequency to finite dimension frequency,the analytic force term to highly differentiable force term.