Electronic Journal of Differential Equations (Jan 2015)
A note on a nonresonance condition at zero for first-order planar systems
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 $$ Ju'=\nabla H(t, u), \quad \nabla H(t, 0) \equiv 0, $$ for which the nonlinearity is resonant both at zero and at infinity, refining and complementing some recent results.