Electron. J. Diff. Equ., Vol. 2015 (2015), No. 21, pp. 1-17.

A note on a nonresonance condition at zero for first-order planar systems

Maurizio Garrione

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.

Submitted November 10, 2014. Published January 27, 2015.
Math Subject Classifications: 34C25, 37E45.
Key Words: Landesman-Lazer condition; rotation number; multiplicity.

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Maurizio Garrione
Dipartimento di Matematica ed Applicazioni
Università di Milano-Bicocca
Via Cozzi 55, I-20125 Milano, Italy
email: maurizio.garrione@unimib.it

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