向量二阶非线性积分微分方程边值问题的奇摄动

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1、2007,27A(6):1133–1140∗SB,;.U7//-'#`H)DE+lns(gkhdfmeqjoipgr350003)℄We.X)C?T_=b'b'1`v{879mVUA!1{q}*!&m*uA_p
t39(C?b'b'1`evMR(2000)b
045Ja05O175.1%FCA^$51003-3998(2007)06-1133-081ZV[1]`%`Z%z~Fwo[>hk
a$>o)W((/,$Z3[2]-

2、

3、okk%`A}>ZUW(,>(℄*)Z%>/,6k%`A}>ZUW(B>Z%>/>^tHso2X,k>ZU1d2X
h=>y,W(℄;B>S`%`Z%Robin/′′′εy=f(t,Ty,y,y,ε),(1.1)a(ε)y(0,ε)−b(ε)y′(0,ε)=α(ε),c(ε)y(1,ε)+d(ε)y′(1,ε)=β(ε)(1.2)>^tH
℄y,f,α(ε),β(ε))n*B>
a(ε),b(ε),c(ε),d(ε))7>*{
ε>0)E
TFdzC[0,1]r

4、>`Z1Ty=ϕ(t,s,ε)y(s)ds,y(t)∈C[0,1].028p

5、)(1.1),(1.2)}>}-}
j#sZUT>0zl)>℄oH>ts,Æw6B$:(H)f(t,x,y,z,ε)∈CN+1([0,1]×R3×[0,ε]),10ϕ(t,s,ε)∈CN+1([0,1]×[0,1]×[0,ε]),0N+1a(ε),b(ε),c(ε),d(ε)∈C([0,ε0]).℄Nl℄lF>
ε0V℄E
a(0)>0,b(0)=0,b(ε)≥0,c(0)>0,d(

6、0)>0;∗im2005-11-16;Gm2006-10-08E-mail:lsr@fjrtvu.edu.cn1134T35TÆVol.27A(H2)fz(t,x,y,z,ε)≥mI>0,fy(t,x,y,z,ε)≥lI>0,f(t,x,y,z,ε)vsx∂fiLipschitz
℄fz=∂zj,i,j=1,2,···,n;m,l)=
I)n×n5+(H3)fvszNagumo
z[0,+∞)r0zV℄>℄>;S{Φ,2{=kf(t,x,y,z,ε)k≤Φ(kzk)

7、7s→∞yS/

8、Φ(s)→∞;(H)′R4"/f(t,Ty0,y0,y0,0)=0,a(0)y(0)=α(0)z[0,1]ro(℄y0(t),℄1Ty0=0ϕ(t,s,0)y0(s)ds.sB>{*{A(t)=(aij(t))∈C[0,1],wFY)hXi122

9、A(t)

10、=ai,j(t),kA(t)k=max

11、A(t)

12、,0≤t≤1i,jEEB>

13、E*)0.21TG:>=2w?}$)y(t,ε)=Y(t,ε)+εu(τ,ε),(2.1)℄Y(t,ε))#
u(τ,ε)"!{
τ=(1−t

14、)/ε,wY(t,ε)=y(t)+εy(t)+ε2y(t)+···,(2.2)012u(τ,ε)=u(τ)+εu(τ)+ε2u(τ)+···.(2.3)012(2.1)}4o(1.1)}
t

15、τ):>
/R0GεY′′(t,ε)=f(t,TY,Y,Y′,ε),(2.4)′′′u(τ,ε)=G(τ,u(τ,ε),u(τ,ε),ε).(2.5)℄′′′′G(τ,u(τ,ε),u(τ,ε),ε)=[f(t,T(Y+εu),Y+εu,Y−u,ε)−f(t,TY,Y,Y,ε)]

16、t=1−ετ.wϕ(t,s,ε),ϕ(1

17、−ετ,s,ε)ε-ybpg`)ϕ(t,s,ε)=ϕ(t,s)+εϕ(t,s)+ε2ϕ(t,s)+···.(2.6)012ϕ(1−ετ,s,τ)=ϕ(τ,s)+εϕ(τ,s)+ε2ϕ(τ,s)+···.(2.7)012(2.2),(2.3)

18、(2.6),(2.7)}4o(2.4),(2.5)}
q{ε}-
jGε.>4>A
0=;yi(t)

19、ui(τ)>Z%0=f(t,Ty,y,y′,0),(2.8)000Z1′′′yi−1=fx(t)ϕ0(t,s)yi(s)ds+fy(t)yi+fz(t)yi+P

20、i,i=1,2,···,N.(2.9)0′′℄Rfx(t),fy(t),fz(t)zD(t,Ty0,y0,y0,0)+h
Pi(t)t,yl(t),yl(t)(l=0,1,···,1i−1),0ϕm(t,s)yl(s)ds(m=0,1,···i;l=0,1,···,i−1)>;S{′′′u0=G0(u0),(