Resonance with respect to the Fucik spectrum
(2000) Electronic Journal of Differential Equations — Vol. 2000, n° 37, p. 1-21 (2000)
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- Abstract
- Let L be a self-adjoint operator on L^2(Omega;R) with Omega a bounded and open subset of {R}^N. This article considers the resonance problem with respect to the Fucik spectrum of L, which means that we study equations of the form Lu = Alpha u^+ - Beta u^- + f(.,u), when the homogeneous equation Lu = Alpha u^+ - Beta u^- 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 Landesman-Lazer conditions. Non-existence results are also given.
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Ben-Naoum, A. K., Fabry, C., & Smets, D. (2000). Resonance with respect to the Fucik spectrum. Electronic Journal of Differential Equations, 2000(37), 1-21. https://hdl.handle.net/2078.5/251967 (Original work published 2000)