Fractional elliptic equations with critical growth and singular nonlinearities
Date
2016-02-23
Authors
Mukherjee, Tuhina
Sreenadh, Konijeti
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Nonlocal operator, Fractional Laplacian, Singular nonlinearities
Citation
Mukherjee, T., & Sreenadh, K. (2016). Fractional elliptic equations with critical growth and singular nonlinearities. Electronic Journal of Differential Equations, 2016(54), pp. 1-23.
Rights
Attribution 4.0 International