Geodesic
A note on a nonresonance condition at zero for first-order planar systems
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce a Landesman-Lazer type nonresonance condition at zero for planar systems and discuss its rotational interpretation. We then show an application concerning multiplicity of T-periodic solutions to unforced Hamiltonian systems like $$ Ju'=\nabla H(t, u), \quad \nabla H(t, 0) \equiv 0, $$ for which the nonlinearity is resonant both at zero and at infinity, refining and complementing some recent results.
Classification : 34C25, 37E45
Keywords: landesman-lazer condition, rotation number, multiplicity 
@article{EJDE_2015__2015__a16,
     author = {Garrione, Maurizio},
     title = {A note on a nonresonance condition at zero for first-order planar systems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a16/}
}
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Garrione, Maurizio. A note on a nonresonance condition at zero for first-order planar systems. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a16/