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.

引用

页码：327 / 349

页数：23

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