Aftabizadeh, A. R.; Gupta, Chaitan P.; Xu, Jian-Ming Existence and uniqueness theorems for three-point boundary value problems. (English) Zbl 0704.34019 SIAM J. Math. Anal. 20, No. 3, 716-726 (1989). The paper deals with the existence and uniqueness of the solutions to the boundary value problems \[ u'''+f(u')u''=g(x,u,u',u'')+e(x),\quad u'(0)=u'(1)=u(\eta)=0\quad (0\leq \eta \leq 1) \] and \[ u'''=g(x,u,u',u'')+e(x),\quad u'(0)=u''(1)=u(\eta)=0\quad (0\leq \eta \leq 1). \] The proofs of the obtained results are based on the Leray-Schauder continuation theorem and Wirtinger-type inequalities. Reviewer: M.Tvrdý Cited in 16 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:third-order boundary value problems; sandwich beam; Leray-Schauder continuation; Wirtinger-type inequalities PDFBibTeX XMLCite \textit{A. R. Aftabizadeh} et al., SIAM J. Math. Anal. 20, No. 3, 716--726 (1989; Zbl 0704.34019) Full Text: DOI