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Landesman-Lazer-type results for first order periodic problems. (English) Zbl 0893.34012
The author gives sufficient conditions for the existence of nonnegative solutions for nonlinear first order periodic problems \[ y'= f(t,y) \quad \text{a.e. on } [0,T],\qquad y(0)=y(T), \] where \(f: [0,T]\times \mathbb{R} \to \mathbb{R}\) is an \(L^1\)-Carathéodory function. The nonlinearity \(f\) is supposed to satisfy a Landesman-Lazer-type condition. Placing less restrictive conditions on \(f\) than M. N. Nkashama and J. Santanilla [J. Differ. Equations 84, 148-164 (1990; Zbl 0693.34011)], the author provides a proof based on a technique iniciated by Mawhin and Ward and obtains a new existence result.
Reviewer: J.Kalas (Brno)

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
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