Staněk, Svatoslav Existence of multiple solutions for some functional boundary value problems. (English) Zbl 0782.34074 Arch. Math., Brno 28, No. 1-2, 57-65 (1992). The problem (1) \(x'''= q(t,x,x',x'')\), \(t\in [0,1]\), \(\alpha(x)=\beta(x')=0\), \(x''(0)= x''(1)\) with \(\alpha\), \(\beta\) continuous, increasing functionals, \(\alpha(0)=\beta(0)=0\), is investigated. Using Schauder’s fixed point theorem sufficient conditions for the existence of (a) at least one solution of (1) with \(x''(t)\geq 0\) on \([0,1]\), (b) at least one solution of (1) with \(x''(t)\leq 0\) on \([0,1]\), (c) at least two different solutions \(x_ 1\), \(x_ 2\) of (1) with \(x_ 1{''}(t)\leq 0\leq x_ 2{''}(t)\) on \([0,1]\) are obtained. The proofs are based on a priori estimates, degree theory and lower and upper solutions. Reviewer: T.Dłotko (Katowice) Cited in 1 Document MSC: 34K10 Boundary value problems for functional-differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:third order functional-differential equation; functional boundary conditions; Schauder’s fixed point theorem; a priori estimates; degree theory; lower and upper solutions PDFBibTeX XMLCite \textit{S. Staněk}, Arch. Math., Brno 28, No. 1--2, 57--65 (1992; Zbl 0782.34074) Full Text: EuDML EMIS