×

Existence and uniqueness theorems for three-point boundary value problems. (English) Zbl 0704.34019

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

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI