摘要
In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].
In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].
作者
Congming LI
Zhigang WU
李从明;吴志刚(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China;Department of Applied Mathematics,University of Colorado Boulder,USA;Department of Applied Mathematics,Donghua University,Shanghai 201620,China)
基金
Partially supported by NSFC(11571233)
NSF DMS-1405175
NSF of Shanghai16ZR1402100
China Scholarship Council
