高阶非线性脉冲泛函微分方程的振动性

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1、2008,28A(1):188–200∗kqhzafnig`Æe%""(&(#!$!'510225)/'r&;eZ7'Tw}℄W";AG86o1AG;i$℄wlpbe Tw}℄W"7'AG ZMR(2000)

2、jt34D}jtoO175.1
^{yA
℄o1003-3998(2008)01-188-131_G%5%{[U[~hÆ91393np9-(4Z9$%p6q9-pS9)+n0

3、A[1−10]9Y{[U9?E!-.-9t,A5%{[U9?E!-.-9n05%{[U9?E[11–13],(Y"Z)5%{[U9?E[14–15],[16].5%Su{[U9?E5A~G5%Su{[U9?E:6
=Wf[6vÆ(A)(B)(C)*9t.&p%905%9YSv{[U<5g395%vlbU9o-65%#
H~?E2rm"5%Sv{[xp[r(t)x(2n−1)(t)]

4、′+p(t)[x(2n−1)(t)]qf(x(t−τ))=0,t≥t,t6=t,0kx(i)(t+)=g(x(i)(t)),i=0,1,···,2n−1,k=1,2···,kk(i)k(1)x(i)(t+)=x(i),00x(t)=φ(t),t∈[t0−τ,t0].x(i−1)(t+h)−x(i−1)(t)x(i)(t)=limkk,kh→0−hifV2006-01-08;DV2007-06-18E-mail:zhcl88@126.com∗Bqh!~B(2006J1-C034

5、1)RNo.1;2<Y5%Sv{[U9?E189x(i−1)(t+h)−x(i−1)(t)x(i)(t+)=limkk,k+hh→0φ:[t0−τ,t0]→RH-h>&
6=fZ+900,tk+1−tk>τ,limt=+∞,x(0)(t)=x(t),nk→∞kTSl6B
:
=WfC"vÆ*(A)f(x)′~(−∞,+∞)Z+xf(x)>0(x6=0),f(x)>0,p(t)≥0

6、6[t0−τ,+∞)Z+3t≥t0,p(s)6[t,+∞)Z

7、~0(i)(i)(B)6(−∞,+∞)Zgk(i)(x)+-6Clak,bk,i=0,1,···,2n−1,8X(i)gk(i)(x)(i)a≤≤b.kxk(C)6[t0−τ,+∞)Zr(t)f+90

8、∞.(2)(i−1)(i−1)(i−1)tr(t)b1b2···bmmZ+∞1Ya(i)kds=+∞tr(s)(i−1)0t00)~(1)d9Xp8X(i)x(i)(t)6[t0,t0+α){tk,k∈N},i=0,1,···,2n−1+(ii)x(t)=φ(t),t∈[t−τ,t],x(i)(t+)=x(i),i=0,1,···,2n−1.0000(iii)6[t0,t0+α

9、){tk,k∈N},x(t)8XU(1)9>d(iv)(i)(i)6tk*x(t)Z.-6Z+x(tk)8XU(1)9>di=0,1,2,···,2n−1,k=1,2,···.0Uzτ>0,φ8XZ>vÆ)+y49UW""<58X(vÆ9+[17]9U
=""<5#X9vÆRCU(1)6[t0,+∞)9Bu-6"
=WfCU(1)6[t0,+∞)Buf-69d2U(1)9~Y?E9Wt=hY~CY~a_7b~?E9Wt(1)d9o-~

10、?E97(1)d~?E91PC={x:R+→R

11、x(t)f+"4t∈R+{tk,k=1,2,···}},R+=[0,+∞).u1[(A)m∈PC1[R,R],0+6tk*m(t)fZ+9k=1,2,···,(A1)0k=1,2,···,t≥t0,′m(t)≤p(t)m(t)+q(t),t6=tk,+m(tk)≤dkm(t