抽象空间中非线性脉冲方程的解及其应用.pdf

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}Wm0;y6eVG3mDAs7^Cmn3Z7Vzt"BanachSEV+Cg0XVqa}Wm=3i0;?-Cy6F-x′′(t)+ω(t)f(t,x(t),x′(t),(Tx)(t),(Sx)(t))=θ,t∈J,t6=t,k′△x

7、t=tk=Ik(x(tk)

8、,x(tk)),(1.1.1)△x′

9、=I(x(t),x′(t)),k=1,2,···,m,t=tkkkkZ1Z1x(0)=a(s)x(s)ds,x(1)=b(s)x(s)ds,00VZtZ1(Tx)(t)=k(t,s)x(s)ds,(Sx)(t)=h(t,s)x(s)ds.(1.1.2)00+++>k∈C[F,R],h∈C[J×J,R],VR=[0,+∞),F={(t,s)∈J×J

10、t≥s}.x(t+)−k1x(tk)$#x(t)3t=tkAV!EV1pEV%V∆x

11、t=tk=x(t

12、+)−x(t−),′′kkH∆x

13、t=tkx(t)3t=tkAV2-i∆x

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15、x′(t))+d(t)I¯(x(t),x′(t)),t∈J,kkkkkkkk0

16、t≥s},f(s,x,y,u,v)3s=0AÆZtZa(Tx)(t)=k(t,s)x(s)ds,(Sx)(t)=h(t,s)x(s)ds,(2.1.2)00+++1∗+∗>k∈C[F,R],h∈C[J×J,R],R=[0,+∞),ak,dk∈C[Jk,R],Jk=[t

17、k,a](k=1,2,···,m).J0=[0,t1],J1=(t1,t2],···,Jm−1=(tm−1,tm],Jm=(tm,a],G0=max{G(t,s)

18、(t,s)∈F},G1=max{G′t(t,s)

19、(t,s)∈F},a∗=k∗∗′∗∗∗′maxt∈J∗ak(t),ak=maxt∈J∗ak(t),dk=maxt∈J∗dk(t),dk=maxt∈J∗dk(t