TY - JOUR
AU - Chen, Hong
AU - Hua, Qiaoqiao
PY - 2023/08/07
Y2 - 2024/02/22
TI - Solutions with multiple peaks for nonlinear Kirchhoff equations on R^3
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 48
IS - 2
SE - Articles
DO - 10.54330/afm.131900
UR - https://afm.journal.fi/article/view/131900
SP - 537-566
AB - <pre>In this paper, we mainly investigate the following nonlinear Kirchhoff equation</pre><pre>\(-\left(\epsilon^2 a+\epsilon b\int_{\mathbb{R}^3}|
abla u|^2\right)\Delta u +u =Q(x)u^{q-1}\), \(u>0\), \(x\in\mathbb{R}^{3}\),<br><br></pre><pre>\(u\to 0\), as \(|x|\to +\infty\),</pre><pre> </pre><pre>where \(a,b>0\) are constants, \(2<q<6\), and \(\epsilon>0\) is a parameter. Under some suitable assumptions on the function \(Q(x)\), we obtain that the equation above has positive multi-peak solutions concentrating at a critical point of \(Q(x)\) for \(\epsilon>0\) sufficiently small, by using the finite dimensional reduction method. Different from the local SchrÃ¶dinger problem, here the corresponding limit problem is a system. Moreover, the nonlocal term brings some new difficulties which involve some technical and complicated estimates.</pre>
ER -