Cabada, Alberto; Sanchez, Luis A positive operator approach to the Neumann problem for a second order ordinary differential equation. (English) Zbl 0871.34014 J. Math. Anal. Appl. 204, No. 3, 774-785 (1996). Summary: The solvability of the second order Neumann problem \[ u''(t)+ cu'(t)+ f(t,u(t))=0, \qquad u'(0)=A,\;u'(R)=B, \] is studied. We suppose that there is a lower solution \(\gamma\) and an upper solution \(\beta\) in the reversed order, and we obtain optimal conditions in \(f\) to assure the existence of a solution lying between \(\beta\) and \(\gamma\). Cited in 25 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34A26 Geometric methods in ordinary differential equations Keywords:second order Neumann problem; lower solution; upper solution PDFBibTeX XMLCite \textit{A. Cabada} and \textit{L. Sanchez}, J. Math. Anal. Appl. 204, No. 3, 774--785 (1996; Zbl 0871.34014) Full Text: DOI