Goel, DivyaGoyal, SarikaSreenadh, Konijeti2022-01-262022-01-262018-03-17Goel, D., Goyal, S., & Sreenadh, K. (2018). First curve of Fucik spectrum for the p-fractional Laplacian operator with nonlocal normal boundary conditions. <i>Electronic Journal of Differential Equations, 2018</i>(74), pp. 1-21.1072-6691https://hdl.handle.net/10877/15216In this article, we study the Fučik spectrum of the p-fractional Laplace operator with nonlocal normal derivative conditions which is defined as the set of all (α, b) ∈ ℝ2 such that ∧n,p (1 - α) (-∆)αpu + |u|p-2u = XΩε/ε (α(u+)p-1 -b(uˉ)p-1) in Ω, Nα,pu = 0 in ℝn \ Ω̅, has a non-trivial solution u, where Ω is a bounded domain in ℝn with Lipschitz boundary, p ≥ 2, n > pα, ε, α ∈ (0, 1) and Ωε ≔ {x ∈ Ω : d(x, ∂Ω) ≤ ε}. We show existence of the first non-trivial curve C of the Fučik spectrum which is used to obtain the variational characterization of a second eigenvalue of the problem defined above. We also discuss some properties of this curve C, e.g., Lipschitz continuous, strictly decreasing and asymptotic behavior and non-resonance with respect to the Fučik spectrum.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalNonlocal operatorFucik spectrumSteklov problemNon-resonanceArticle