Banach空间四阶周期边值问题正解的存在性.pdf

文档介绍：???????Б2013,28(2): 165-170Banach??????ш????????????(???????????,????745000)??:???Banach??E??????ш???:(u(4)(t)?ξu00(t) +ηu(t) =f(t, u(t)),06t61,u(i)(0) =u(i)(1), i= 0,1,2,3??????,??f: [0,1]×P→P??,P?E????,ξ, η∈R???0< η<(ξ2+2π2)2, ξ>?2π2,ηπ+ξπ+1>0.???????????????????????????????????????.???:????ш???;о??;??;????;??????????: ; ?????: A??щ?: 1000-4424(2013)02-0165-006§1???E???Banach??,????P????,?????N,?I= [0,1],Ч???E??????ш???:(u(4)(t)?ξu00(t) +ηu(t) =f(t, u(t)), t∈I,u(i)(0) =u(i)(1), i= 0,1,2,3(1)??????.??f:I×P→P??,ξ, η∈R???0< η<(ξ2+2π2)2, ξ>?2π2,ηπ+ξπ+1>0.???????э???????????(1)???,????????????????[1-6],???????????????????????????????.????????Banach?????????ш?????????.Ч????Banach??????????????????????(1)??????.??(1)?????u∈C4(I, E)????(1),??u(t)> θ,0< t <??????????????????????,??????????????????,?????????????.????????????????????,?????f???????????.Ч??????????????:????:2012-11-08????: 2013-05-17????:????????????(XYZK1109)166???????Б?28??2?(H0)??R>0,f(I×PR)??,?????L=LR∈(0,η4)????t∈I, D?PR,?α(f(t, D))6Lα(D).??PR={x∈P:kxk6R}.???Banach?????????????,????????f?????????,???[7].Ч??????????????[8]????f??????.§2?С???C(I, E)????I???E???????ο??kuk= maxt∈Iku(t)k???Banach??,?C(I, P) ={u∈C(I, E)|u(t)∈P, t∈I},?C(I, P)?C(I, E)?????,??????N,?????C(I, E)???6?C(I, P)??.??????ш???:(u(4)(t)?ξu00(t) +ηu(t) =θ, t∈I,u(i)(0) =u(i)(1), i= 0,1,2, u(3)(0)?u(3)(