A class of semilinear elliptic equations on groups of polynomial growth

被引：11
|
作者：
Hua, Bobo [1 ,2 ]
Li, Ruowei [3 ]
Wang, Lidan [3 ]
机构：
[1] Fudan Univ, Sch Math Sci, LMNS, Shanghai 200433, Peoples R China
[2] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China
[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 363卷
关键词：
Semilinear elliptic equation; Cayley graph; Groups of polynomial growth; Palais-Smale sequences; CONCENTRATION-COMPACTNESS PRINCIPLE; SCALAR FIELD-EQUATIONS; KAZDAN-WARNER EQUATION; POSITIVE SOLUTIONS; NONLINEAR EQUATIONS; GAUSSIAN CURVATURE; EXPONENTIAL-GROWTH; EXISTENCE; CONVERGENCE; CALCULUS;
D O I：
10.1016/j.jde.2023.03.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the semilinear elliptic equation -Delta u + a(x)vertical bar u vertical bar(p-2) u - b(x)vertical bar u vertical bar(q-2) u = 0 on a Cayley graph of a discrete group of polynomial growth with the homogeneous dimension N >= 1, where 2 <= p < q < +infinity. We first prove the existence of positive solutions to the above equation with constant coefficients (a) over bar, (b) over bar. Then we establish a decomposition of Palais-Smale sequences for the functional with variable coefficients a(x), b(x), which tend to the constants (a) over bar, (b) over bar at infinity. (c) 2023 Elsevier Inc. All rights reserved.
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页码：327 / 349
页数：23
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