Pei, Minghe; Lü, Xuezhe Existence of solutions for two classes of nonlinear third-order three-point boundary values. (Chinese. English summary) Zbl 1340.34071 J. Beihua Univ., Nat. Sci. 16, No. 1, 1-4 (2015). Summary: We investigate the existence of solutions for nonlinear third-order differential equations \[ x'''=f(t, x, x', x''), t\in [0,1] \] subject to the following two sets of three-point boundary problem conditions: \[ x(0)=0, ax'(0)-bx''(0)=0, x'(1)=\alpha x'(\xi) \] and \[ x'(0)=\beta x'(\eta), x(1)=0, cx'(1)+dx''(1)=0. \] By using the Leray-Schauder degree theory, the existence of solutions for the above boundary value problems are given. MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:Leray-Schauder degree theory; Nagumo condition; boundary value problem; existence PDFBibTeX XMLCite \textit{M. Pei} and \textit{X. Lü}, J. Beihua Univ., Nat. Sci. 16, No. 1, 1--4 (2015; Zbl 1340.34071)