We prove a result of Ambrosetti-Prodi type for the scalar periodic ODE $x'=f(t,x)-s$, where, seemingly for the first time in the literature, $f(cdot,x) $ is allowed to have indefinite sign as $|x| o+infty$. Our result requires that $f$ satisfies a one-sided growth control; in case such a control fails, non-existence occurs for large $s>0$, although multiplicity of solutions can still be detected provided $f(cdot,0)=0$ and $s>0$ is small enough.
Titolo: | On the periodic Ambrosetti–Prodi problem for a class of ODEs with nonlinearities indefinite in sign |
Autori: | OMARI, PIERPAOLO (Corresponding) |
Data di pubblicazione: | 2020 |
Data ahead of print: | 6-lug-2020 |
Stato di pubblicazione: | Pubblicato |
Rivista: | |
Abstract: | We prove a result of Ambrosetti-Prodi type for the scalar periodic ODE $x'=f(t,x)-s$, where, seemingly for the first time in the literature, $f(cdot,x) $ is allowed to have indefinite sign as $|x| o+infty$. Our result requires that $f$ satisfies a one-sided growth control; in case such a control fails, non-existence occurs for large $s>0$, although multiplicity of solutions can still be detected provided $f(cdot,0)=0$ and $s>0$ is small enough. |
Handle: | http://hdl.handle.net/11368/2969071 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aml.2020.106622 |
URL: | https://www.sciencedirect.com/science/article/pii/S0893965920303037 |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
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