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 ...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].展开更多
基金Partially supported by NSFC(11571233)NSF DMS-1405175+1 种基金NSF of Shanghai16ZR1402100China Scholarship Council
文摘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].
