Abstract
In this article, we study the Fučik spectrum of the fractional Laplace operator which is defined as the set of all \({(\alpha, \beta)\in \mathbb{R}^2}\) such that
has a non-trivial solution u, where \({\Omega}\) is a bounded domain in \({\mathbb{R}^n}\) with Lipschitz boundary, n > 2s, \({s \in (0, 1)}\) . The existence of a first nontrivial curve \({\mathcal{C}}\) of this spectrum, some properties of this curve \({\mathcal{C}}\), e.g. Lipschitz continuous, strictly decreasing and asymptotic behavior are studied in this article. A variational characterization of second eigenvalue of the fractional eigenvalue problem is also obtained. At the end, we study a nonresonance problem with respect to the Fučik spectrum.
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Goyal, S., Sreenadh, K. On the Fučik spectrum of non-local elliptic operators. Nonlinear Differ. Equ. Appl. 21, 567–588 (2014). https://doi.org/10.1007/s00030-013-0258-6
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DOI: https://doi.org/10.1007/s00030-013-0258-6