Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N
Files
Date
2018-01-10
Authors
Jin, Lingyu
Fang, Shaomei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the fractional elliptic equation with critical Sobolev-Hardy nonlinearity
(-∆)α u + α(x)u = |u|2*s - 2u/|x|s + k(x)|u|q-2u,
u ∈ Hα (ℝN),
where 2 < q < 2*, 0 < α < 1, N > 4α, 0 < s < 2α, 2*s = 2(N - s)/(N - 2α) is the critical Sobolev-Hardy exponent, 2* = 2N/(N - 2α) is the critical Sobolev exponent, α(x), k(x) ∈ C(ℝN). Through a compactness analysis of the functional associated, we obtain the existence of positive solutions under certain assumptions on α(x), k(x).
Description
Keywords
Fractional Laplacian, Compactness, Positive solution, Unbounded domain, Sobolev-Hardy nonlinearity
Citation
Jin, L., & Fang, S. (2018). Existence of solutions for a fractional elliptic problem with critical Sobolev-Hardy nonlinearities in R^N. <i>Electronic Journal of Differential Equations, 2018</i>(12), pp. 1-23.
Rights
Attribution 4.0 International