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 (fourmula presented) for which the nonlinearity is resonant both at zero and at infinity, refining and complementing some recent results.
Garrione, M. (2015). A note on a nonresonance condition at zero for first-order planar systems. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015(21), 1-17.
A note on a nonresonance condition at zero for first-order planar systems
GARRIONE, MAURIZIO
2015
Abstract
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 (fourmula presented) for which the nonlinearity is resonant both at zero and at infinity, refining and complementing some recent results.
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