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A positive operator approach to the Neumann problem for a second order ordinary differential equation. (English) Zbl 0871.34014

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 \(\gamma\).

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
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