Classification of nonnegative classical solutions to third-order equations

被引:74
作者
Dai, Wei [1 ]
Qin, Guolin [1 ]
机构
[1] Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100083, Peoples R China
关键词
Fractional Laplacians; Odd order; Positive classical solutions; Radial symmetry; Uniqueness; Liouville theorems; SEMILINEAR ELLIPTIC-EQUATIONS; FRACTIONAL LAPLACIAN; LOCAL BEHAVIOR; UNIQUENESS; SYMMETRY; SOBOLEV; REGULARITY; THEOREMS; R-3;
D O I
10.1016/j.aim.2018.02.016
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we are concerned with the third-order equations (1.1) and (1.11) with critical or subcritical nonlinearities. By applying the method of moving planes to the third-order PDEs (1.1) and (1.11), we prove that nonnegative classical solutions u to (1.1) and (1.11) are radially symmetric about some point x(0) is an element of R-n and derive the explicit forms for u in the critical case. We also prove the non-existence of nontrivial nonnegative classical solutions in the subcritical cases (see Theorem 1.1 and Theorem 1.3). (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码:822 / 857
页数:36
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