an existence theorem is established for the following elastic beam equation in which nonlinear term contains all order derivativesu4(t)+f(t
u(t)
u′(t)
u″(t)
u″(t))=e(t)
0≤t≤1
u(0)=u(1)=u′(0)=u′(1)=0.In the material mechanics
the equation describes the deformation of an elastic beam whose both ends are fixed.Our results show that the equation has at least one solution provided the nonlinear term satisfies a linear growth restriction.
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references
A garw a l R P,Chow Y M.Iterative m ethods for fourth order boundary va lue prob lem s[J].J Com pu t A pp lM ath,1984,10(2):203-217.
D a lm asso R.U n iqueness of pos itive so lu tions for som e non linear fourth-order equations[J].J M th A na l A pp l,1996,201(1):152-168.
Lou B endong.Pos itive so lu tions for non linear e lastic beam m ode ls[J].In t JM ath M ath Sc i,2001,27(6):365-375.
M a R uyun,W u Hongp ing.Pos itive so lu tions of fourth-order tw o-po in t boundary va lue prob lem[J].A cta M athSc ien tia,2002,22A(2):244-249,in Ch inese.
Y ao Q ing liu.Ex istence and m u ltip lic ity of so lu tions for a class of non linear e lastic beam equations w ith bounded-be lownon linearity[J].A cta M ath A pp l S in ica,2004,27(1):117-122,in Ch inese.
Y ao Q ing liu.Pos itive so lu tions for e igenva lue prob lem s of fourth-order e lastic beam equations[J].A pp lM ath L etters,2004,17(2):237-243.
G upta C P.Ex istence and un iqueness theorem s for the bend ing of an e lastic beam equation[J].A pp licab le A na lys is,1988,26(3):289-304.
M a R uyun.Ex istence and un iqueness theorem s for som e fourth-order non linear boundary va lue prob lem s[J].In ternatJM th M ath Sc i,2000,23(11):783-788.