Existence of solutions of three-point boundary value problems for nonlinear fourth order differential equation

✍ Scribed by Gao Yongxin

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 358 KB
• Volume: 17
• Category: Article
• ISSN: 0253-4827
• DOI: 10.1007/bf00119755

✦ Synopsis

In this peqwr, tlw author uses the methods in [I, 2] to study tile existence of ,~ohttions of three ~mini houndarv vahte problems.[or mmlinear fottrth order d(fferential CtIIHIIiOll tl ~ --" [(t, Y, Y', Y", Y'" ) (~) with the I~otltt(hllT conditions g(ll(a) ,Yt(a) ,YtP(a), Y~lt(a)) = 0, h(y(b),ytr(b))= 0 1 y~(.b)--bl, k(y(c),yr(c),p"(c),y"~(c))-~O ,[ For the houmlarv vahw proldems of mmlinear (ourth order d(ff'erential equation yo)~ f( t ,y,yt, yo, y., ) many results hare been given at the l,'esent lime, Bttt the existence of so/utiol~s of boumktrv ralue prohh,m (.). (~-.) studied in this paper has m~t been involved by • the aho|,e researches. Moreorer, the corolhtrv of the important theorem in this paper, i, e. existence qf solutions o/' the hounchul" vahw problem of equation (~) with the following boumhtrl" conditions aov(a)+awr(a)+ aay"(a)+ a3Y"t(a) = Yo, " boy(b)+ b,y"(b) = Yi V(b)=~Z/z, cw(c)+ cw'(c)+ c,U"(c)+ cw'"(c)-'-ll3has not been dealt with io previous.work.~.