Resonance with Respect to the Fucik Spectrum
Date
2000-05-17
Authors
Ben-Naoum, A. K.
Fabry, C.
Smets, Didier
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Let 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.
Description
Keywords
Resonance, Jumping nonlinearity, Landesman-Lazer conditions
Citation
Ben-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.
Rights
Attribution 4.0 International