Symmetry of solutions for a fractional p-Laplacian equation of Choquard type

被引:7
作者
Phuong Le [1 ,2 ]
机构
[1] Ton Duc Thang Univ, Div Computat Math & Engn, Inst Computat Sci, Ho Chi Minh City, Vietnam
[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
关键词
Choquard equations; fractional p-Laplacian; symmetry of solutions; method of moving planes; POSITIVE SOLUTIONS; MAXIMUM-PRINCIPLES; LIOUVILLE THEOREM; ELLIPTIC PROBLEM; CLASSIFICATION; REGULARITY; UNIQUENESS; EXISTENCE; STATE;
D O I
10.1142/S0129167X20500263
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let 0 < s < 1, 0 < ( )alpha < n, p > 2, q > 1, r > 0 and u be a positive solution of the equation (-Delta)(p)(s)u = (1/vertical bar x vertical bar(n-alpha) * u(q)) u(r )in R-n. We prove that if u satisfies some decay assumption at infinity, then u must be radially symmetric and monotone decreasing about some point in R-n. Instead of using equivalent fractional systems, we exploit a generalized direct method of moving planes for fractional p-Laplacian equations with nonlocal nonlinearities. This new approach enables us to cover the full range 0 < alpha < n in our results.
引用
收藏
页数:14
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