【摘要】 该文研究了一类带有凸非线性项的分数阶Laplace方程的解的对称性问题,得到:若非线性项关于解严格凸,则该方程在球或环形区域上的Morse指数为1的全局弱解是轴对称的.更多还原

【Abstract】 In this paper,we investigate the symmetry property of solutions of the fractional Laplacian with convex nonlinearities.The main result is that all entire weak solutions of the above problem of index 1 on the ball or the annular domain are axially symmetric if the nonlinearity is strictly convex with respect to the solution.更多还原