Mukherjee, TuhinaSreenadh, Konijeti2023-06-142023-06-142016-02-23Mukherjee, T., & Sreenadh, K. (2016). Fractional elliptic equations with critical growth and singular nonlinearities. Electronic Journal of Differential Equations, 2016(54), pp. 1-23.1072-6691https://hdl.handle.net/10877/16928In this article, we study the fractional Laplacian equation with critical growth and singular nonlinearity (-∆)su = λα(x)u-q + u2*s-1, u > 0 in Ω, u = 0 in ℝn\Ω, where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, n > 2s, s ∈ (0, 1), λ > 0, 0 < q ≤ 1, θ ≤ α(x) ∈ L∞(Ω), for some θ > 0 and 2*s = 2n/n-2s. We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalNonlocal operatorFractional LaplacianSingular nonlinearitiesArticle