01079nas a2200121   4500008004100000245007600041210006900117300001400186490000700200520062100207100002300828856010600851       2011                        eng d00aResonance and Landesman-Lazer conditions for first order systems in R^20 aResonance and LandesmanLazer conditions for first order systems   a153–1600 v663 a<p>The first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].</p>1 aGarrione, Maurizio  uhttps://www.math.sissa.it/publication/resonance-and-landesman-lazer-conditions-first-order-systems-r2