Normalized solutions for Kirchhoff-Carrier type equation

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>