Fractional elliptic equations with critical exponential nonlinearity

Advances in Nonlinear Analysis

article

Jacques Giacomoni¹  Pawan Kumar Mishra²  K. Sreenadh² 

[1] Avenue de l'Université;Department of Mathematics, Indian Institute of Technology Delhi

关键词: Trudinger–Moser inequality;    square root of laplacian;    Nehari manifold;   

DOI  :  10.1515/anona-2015-0081

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We study the existence of positive solutions for fractional elliptic equations of the type (-Δ) 1/2 u = h ( u ), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like e u 2 as u → ∞ . Here (-Δ) 1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.

【 授权许可】

CC BY