Wang, Libo; Pei, Minghe Existence and uniqueness for nonlinear third-order two-point boundary value problems. (English) Zbl 1188.34027 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 14, No. 3, 321-332 (2007). Summary: The upper and lower solutions method, Leray-Schauder degree theory and differential inequality technique are employed to establish existence and uniqueness results for the class of nonlinear third-order two-point boundary value problems with one-sided Nagumo condition. \[ x''' =f(t,x, x', x"),\quad a<t<b, \tag{1} \]\[ x(a) = A,\tag{2} \]\[ g(x'(a))-[x''(a)]^p=B,\tag{3} \]\[ h(x(b),x'(b))+[x''(b)]^q=C,\tag{4} \]where \(A, B,C\in\mathbb R\), \(f(t,x,y,z) : [a, b]\times \mathbb R^3\mathbb R\) is continuous, \(g(y) : \mathbb R\to\mathbb R\) is continuous, \(h(x,y):\mathbb R^2\to\mathbb R\) is continuous and decreasing on \(x\), \(p\), \(q\) are odd numbers. Cited in 2 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:one-sided Nagumo condition; upper and lower solutions method; Leray-Schauder degree theory PDFBibTeX XMLCite \textit{L. Wang} and \textit{M. Pei}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 14, No. 3, 321--332 (2007; Zbl 1188.34027)