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Comparison of two definitions of lower and upper functions associated to nonlinear second order differential equations. (English) Zbl 1039.34014
Consider the second-order scalar differential equation \((*) \;u'' = f(t,u,u').\) The author compares two definitions of upper and lower solutions to \((*)\) that are due to I. Rachůnková and M. Tvrdý [J. Inequal. Appl. 6,199–226 (2001; Zbl 1039.34013)] and due to C. Fabry and P. Habets [Nonlinear Anal., Theory Methods Appl. 10, 985–1007 (1986; Zbl 0612.34015)]. He shows how the upper and lower solutions of both definitions are related.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
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