Affiliation:
1. School of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan 418008, China
2. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, China
Abstract
<abstract><p>In this paper, we study the following Kirchhoff-Carrier type equation</p>
<p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\left(a+bM\left(|\nabla u|_{2}, |u|_{\tau}\right)\right)\Delta u-\lambda u = |u|^{p-2}u, \quad \ {\rm in}\ \mathbb{R}^{3}, $\end{document} </tex-math></disp-formula></p>
<p>where $ a, \ b > 0 $ are constants, $ \lambda\in \mathbb{R}, \ p\in (2, 6) $. By using a minimax procedure, we obtain infinitely solutions $ (v^{b}_{n}, \lambda_{n}) $ with $ v^{b}_{n} $ having a prescribed $ L^{2} $-norm. Moreover, we give a convergence property of $ v_{n}^{b} $ as $ b\rightarrow 0^{+} $.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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