一类单参数发展方程的时间周期解

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1、@390@5eLLVol.39,No.51996_9sACTAMATHEMATICASINICASept.,1996Q7#D)X+%C2>5%.A1?I(Mxam(z@f1M
2r430074)duWO:^quwl}jdih;fgi_dt=F(t,µ,u)d
p~sdj;netyz;cby`le

2、vdrk03!gi_;~s;j;;{ow;e1SN,PNzU#du=F(t,µ,u)(1.1)dtd.wFt-CF;fµ(;u(x,t)qkYBanach:Ep={u(t):u∈L2((0,T);E),u(0)

3、=u(T)},ME10SF(t,µ,u)X F;F:E1×R×R→E1,lFjkµtu4(4C][1]).+%;~Hwµ,FhF(t,µ,0)=0,U#(1.1)hcQdu=0.∗∗A(µ)=Fu(t,µ.0),A0=Fu(t,0,0),A1=Fuµ(t,0,0),JA(µ)=Fu(t,µ,0)A(µ)6OU#(1.1)jkcQu=0 F

4、/dv=A(µ)v,(1.2)dty

5、EY4;d&cQPb-VcVw?~0Sf'z4UPapC?W;wcQPb-K!^';hCXcQdYh&w?;0SHdYh-CF&EP;wxVd&VcbfD1994`10t5y8
1995`11t20y8H_amv7M#@Z674KK3902/TZσ(µ)Uu=0$H'LkbfI);0SW/(1.3)hVcih1nJJ0S9;z2πiknσ=ξ+iηFloquet;yHwu;k,σ+TUFloquet;z7(H)(i)d1/(1.3)hVcih

6、σ(µ),B(µ)=−dt+A(µ)3ih(ii)σ(0)=0,5µ<0σ<0,5µ>0σ>0;σ(µ)jkµw8&(iii)/(1.3)fmihNwcU]w7;5µ<0;cQdu=0-C;J5µ)oqBJ"µ>0;u=0Pb-)d∗d∗7U0SH(H1(ii)d&&VVB0=−dt+A0,MB0=dt+A0,yB∗0C]o(X={u(t):u∈E1,ujkt8&lu(t)kA0C]o},B0C]o(Y={v(t):v∈L2((0,T);E∗),v(0)=v(T),v∗jkt8&lv(t)kA0C

7、]o}.`&]
Ta,b=(a(·,s),b(·,s))ds.a∈L2((0,T),E),b∈L2((0,T),E∗).E0∗RhB0u,v=u,B0v.∗∗Mφ0B0

8、φ∗.∗∗σ007B(0)=A1,B0φ0=0,yX:3,<*$[=-@4$"VFPL(H1)"E;U#(1.1)cQdwµ=0(Pb-HB0z7(H2).wλVcvΛ⊂C,:λ∈Λ;B0hVc$pRλ:E1→X,lRλjkλ4d−∆+q~ch);Dzda3dt+.h~FbfD.H.[2,3]Sattinger>UPQ*XcQd.w'VF8d&7J`?∗φR83.1Pu=u,φ007B0L:"d;Q=I−P7B0o"dPtQFXh!"d

9、l.wVch!K:E1→X,:KB0=Q.Y:6OU#B0u=f.(3.1)Y73λ∈Λ.(3.1)B"(λ−B0)u=λu−f
}u−λRλu=−Rλf.(3.2)gkRλE17Xh!;hhRλfX≤CfE1.7φ0QU#φ0−λRλφ0=0,∗_+(3.2)HwuiGF8^qBanach:X1={u∈E1:u,φ0=0},X1Sq(5eA0yW=4O{V$<e

10、u∈X1,yRλu,φ0=u,Rλφ0=u,λφ0=λu,φ0=0,YRλ

11、:X1→X