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

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.

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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