CRITICAL GROWTH PROBLEMS FOR 1/2-LAPLACIAN IN R

被引：14

作者：

Giacomoni, J. ^{[1
]}

Mishra, P. K. ^{[2
]}

Sreenadh, K. ^{[2
]}

机构：

[1] LMAP UMR CNRS 5142, Bat IPRA,Ave Univ, F-64013 Pau, France

[2] Indian Inst Technol Delhi, New Delhi 16, India

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2016年 / 8卷 / 03期

关键词：

Trudinger-Moser inequality; square root of Laplacian; Kirchhoff;

D O I：

10.7153/dea-08-15

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of weak solutions for fractional elliptic equations of the type (-Delta)(1/2)u + V(x)u = h(u), u > o in R where h is a real valued function that behaves like e(u2) as u -> infinity and V( x) is a positive continuous unbounded function. Here (-Delta) 1 2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. We also study the corresponding critical exponent problem for the Kirchhoff equation [GRAPHICS] where f(u) behaves like e(u2) as u -> infinity and f(u) similar to u(theta) , with theta > 3, as u -> 0

引用

页码：295 / 317

页数：23

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