We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.
Fonda, A., Garrione, M. (2011). Nonlinear resonance: A comparison between landesman-lazer and ahmad-lazer-paul conditions. ADVANCED NONLINEAR STUDIES, 11(2), 391-404 [10.1515/ans-2011-0209].
Nonlinear resonance: A comparison between landesman-lazer and ahmad-lazer-paul conditions
GARRIONE, MAURIZIO
2011
Abstract
We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.
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