Existence of three solutions for Kirchhoff nonlocal operators of elliptic type
نویسنده
چکیده
In this paper, we prove the existence of at least three solutions to the following Kirchhoff nonlocal fractional equation: M (∫ Rn×Rn |u(x)− u(y)| K(x− y)dxdy − ∫ Ω |u(x)|dx ) ((−∆)u− λu) ∈ θ(∂j(x, u(x)) + μ∂k(x, u(x))), in Ω, u = 0, in R \ Ω, where (−∆) is the fractional Laplace operator, s ∈ (0, 1) is a fix, λ, θ, μ are real parameters and Ω is an open bounded subset of R, n > 2s, with Lipschitz boundary. The approach is fully based on a recent three critical points theorem of Teng [K. Teng, Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators, Nonlinear Anal. Real World Appl. 14(2013), 867–874]. AMS subject classifications: 49J52, 35A15, 34A08
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