Fractional elliptic equations with critical exponential nonlinearity

Advances in Nonlinear Analysis

卷:5

Kumar Mishra Pawan¹  Sreenadh K.¹  Giacomoni Jacques² 

[1] Department of Mathematics, Indian Institute of Technology Delhi,Hauz Khaz, New Delhi-16, India;

[2] LMAP (UMR CNRS 5142) Bat. IPRA, Avenue de l'Université, F-64013 Pau, France;

关键词: trudinger–moser inequality;    square root of laplacian;    nehari manifold;    35j20;   

DOI  :  10.1515/anona-2015-0081

来源: DOAJ

【 摘 要 】

We study the existence of positive solutions for fractional elliptic equations of the type(-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1)where h is a real valued function that behaves like eu2 asu → ∞ . Here (-Δ)1/2 is thefractional Laplacian operator. We show the existence ofmountain-pass solution when the nonlinearity is superlinear neart = 0. In case h is concave near t = 0, we show the existence ofmultiple solutions for suitable range of λ by analyzing thefibering maps and the corresponding Nehari manifold.

【 授权许可】

Unknown