Geodesic
A note on a nonresonance condition at zero for first-order planar systems
Electronic journal of differential equations, Tome 2015 (2015)
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},
     year = {2015},
     volume = {2015},
     zbl = {1326.34070},
     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/