In this paper we study the periodic boundary value problem associated with a first order ODE of the form x' + g(t, x) = s where s is a real parameter and g is a continuous function, T-periodic in the variable t. We prove an Ambrosetti-Prodi type result in which the classical uniformity condition on g(t, x) at infinity is considerably relaxed. The Carathéodory case is also discussed.
A periodic problem for first order differential equations with locally coercive nonlinearities / Sovrano, E.; Zanolin, F.. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 49:(2017), pp. 335-355. [10.13137/2464-8728/16219]
A periodic problem for first order differential equations with locally coercive nonlinearities
Sovrano E.;
2017
Abstract
In this paper we study the periodic boundary value problem associated with a first order ODE of the form x' + g(t, x) = s where s is a real parameter and g is a continuous function, T-periodic in the variable t. We prove an Ambrosetti-Prodi type result in which the classical uniformity condition on g(t, x) at infinity is considerably relaxed. The Carathéodory case is also discussed.
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