Ben-Naoum, A. K.Fabry, C.Smets, Didier2019-12-112019-12-112000-05-17Ben-Naoum, A. K., Fabry, C., & Smets, D. (2000). Resonance with respect to the Fucik spectrum. <i>Electronic Journal of Differential Equations, 2000</i>(37), pp. 1-21.1072-6691https://hdl.handle.net/10877/9050Let L be a self-adjoint operator on L2 (Ω; ℝ) with Ω a bounded and open subset of ℝN. This article considers the resonance problem with respect to the Fučík spectrum of L, which means that we study equations of the form Lu = αu+ - βu- + ƒ(•, u), when the homogeneous equation Lu = αu+ - βu- has non-trivial solutions. Using the computation of degrees that are not necessarily +1 or -1, we present results about the existence of solutions. Our results are illustrated with examples and can be seen as generalizations of Landseman-Lazer conditions. Non-existence results are also given.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalResonanceJumping nonlinearityLandesman-Lazer conditionsArticle