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Some remarks on uniqueness of positive solutions to Kirchhoff type equations
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-09-04 , DOI: 10.1016/j.aml.2021.107642
Ke Wu 1 , Fen Zhou 1 , Guangze Gu 1
Affiliation  

In this paper we study the uniqueness of positive solutions of the nonlinear Kirchhoff type equations in arbitrary dimension N: (P)(a+bRN|u|2dx)Δu+u=|u|p1uinRN,where a0,b>0, 1<p<21 and 2=+ if N=1,2, 2=2NN2 if N3. By converting problem (P) to a system which contains a semi-linear problem, we obtain uniqueness results of positive solutions of (P). The degenerate case of the Kirchhoff type problem (that is, a=0) is also considered. As we shall see, the uniqueness of solutions of (P) depends on parameters a, b and the space dimension N.



中文翻译:

关于基尔霍夫型方程正解唯一性的若干注解

在本文中,我们研究了任意维数非线性 Kirchhoff 型方程正解的唯一性 N)-(一种+电阻N||2dX)Δ+=||-1电阻N,在哪里 一种0,>0, 1<<2-12=+ 如果 N=1,2, 2=2NN-2 如果 N3. 通过转换问题() 对于包含半线性问题的系统,我们得到正解的唯一性结果 (). Kirchhoff 类型问题的退化情况(即,一种=0) 也考虑。正如我们将看到的,解的唯一性() 取决于参数 一种, 和空间维度 N.

更新日期:2021-09-22
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