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. <i>Electronic Journal of Differential Equations, 2016</i>(54), pp. 1-23.

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Attribution 4.0 International

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