EXISTENCE AND SYMMETRY RESULTS FOR A SCHRODINGER TYPE PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

被引：216
|
作者：
Dipierro, S. [1 ]
Palatucci, G. [2 ]
Valdinoci, E. [3 ]
机构：
[1] SISSA, Sect Math Anal, Via Bonomea 265, I-34136 Trieste, Italy
[2] Univ Parma, Dipartimento Matemat, I-43124 Parma, Italy
[3] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy
来源：
MATEMATICHE | 2013年 / 68卷 / 01期
关键词：
Nonlinear problems; fractional Laplacian; fractional Sobolev spaces; critical Sobolev exponent; spherical solutions; ground states;
D O I：
10.4418/2013.68.1.15
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper deals with the following class of nonlocal Schrodinger equations (-Delta)(s)u+u - |u|(p-1)u in R-N; for s is an element of (0, 1). We prove existence and symmetry results for the solutions u in the fractional Sobolev space H-s(R-N). Our results are in clear accordance with those for the classical local counterpart, that is when s = 1.
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页码：201 / 216
页数：16
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