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A generalized upper and lower solutions method and multiplicity results for nonlinear first-order ordinary differential equations. (English) Zbl 0674.34009
Summary: We introduce a generalized upper and lower solutions method for the solvability of first-order ordinary differential equations \(u'(t)=f(t,u(t))\), \(u(0)=u(1)\) in order to cover the case when the function f satisfies Carathéodory conditions. This method is then applied to obtain multiplicity results when the nonlinearity f interacts with the real eigenvalue of the linearized problem. Our proofs are based on differential inequalities and classical Leray-Schauder degree.

34A34 Nonlinear ordinary differential equations and systems, general theory
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