Existence of solutions for a quasilinear elliptic system with local nonlinearity on DOUBLE-STRUCK CAPITAL RN

被引：3

作者：

Zhang, Xingyong ^{[1
,2
]}

Liu, Cuiling ^{[1
]}

机构：

[1] Kunming Univ Sci & Technol, Fac Sci, Kunming 650500, Yunnan, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2021年 / 44卷 / 17期

关键词：

cutoff technique; local nonlinearity near origin; Moser iteration technique; mountain pass theorem; quasilinear elliptic system; POSITIVE SOLUTIONS; EQUATIONS;

D O I：

10.1002/mma.7617

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence of solutions for a class of quasilinear elliptic system. By developing the Moser iteration technique, we obtain that system has a nontrivial solution (u(lambda), v(lambda)) with ||(u(lambda), v(lambda))||(infinity) <= 2 for every lambda large enough when the nonlinear term F satisfies some growth conditions only in a circle with center 0 and radius 4, and the families of solutions {(u(lambda), v(lambda))} satisfy that ||(u(lambda), v(lambda)) || -> 0 as lambda -> infinity. Moreover, because the interaction of u and v in elliptic system causes that the estimate of ||u||(infinity) cannot vary with ||u||, the conclusion for the elliptic system is weaker than the corresponding result for the quasilinear elliptic equation, which is given in the end as a comparison.

引用

页码：13186 / 13212

页数：27

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