In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution...In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution is radially symmetric.展开更多
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
文摘In this paper, we are concerned with a positive solution of the non-homogeneous A-Laplacian equation in an open bounded connected domain. We use moving planes method to prove that the domain is a ball and the solution is radially symmetric.
基金Supported by the Anhui Provincial Natural Science Foundation(1408085MA02,1308085MA01,1508085QA01)the Key Foundation of Anhui Education Bureau(KJ2012A019,KJ2013A028,KJ2014A010)+2 种基金the Research Fund for Doctor Station of Ministry of Education of China(20113401110001)the 211 Project of Anhui University(KJJQ1101,02303303-33030011,02303902-39020011,J18520207,XJYJXKC04)the National Natural Science Foundation of China(11271371,11301004,51479215)
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].
