We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman-Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer-Fučik spectrum. © 2010 Elsevier Inc.

Fonda, A., Garrione, M. (2011). Double resonance with Landesman-Lazer conditions for planar systems of ordinary differential equations. JOURNAL OF DIFFERENTIAL EQUATIONS, 250(2), 1052-1082 [10.1016/j.jde.2010.08.006].

Double resonance with Landesman-Lazer conditions for planar systems of ordinary differential equations

GARRIONE, MAURIZIO
2011

Abstract

We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman-Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry's results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer-Fučik spectrum. © 2010 Elsevier Inc.
Articolo in rivista - Articolo scientifico
Double resonance; Landesman-Lazer conditions; Nonlinear planar systems; Analysis
English
2011
250
2
1052
1082
none
Fonda, A., Garrione, M. (2011). Double resonance with Landesman-Lazer conditions for planar systems of ordinary differential equations. JOURNAL OF DIFFERENTIAL EQUATIONS, 250(2), 1052-1082 [10.1016/j.jde.2010.08.006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/62271
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