| Autor: |
Renhua Chen, Li Wang, Xin Song |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2024, Iss 48, Pp 1-19 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2024.1.48 |
| Popis: |
This paper considers the existence of multiple normalized solutions of the following $(2,q)$-Laplacian equation: \begin{equation*} \begin{cases} -\Delta u-\Delta_q u=\lambda u+h(\epsilon x)f(u), &\mathrm{in}\ \mathbb{R}^{N},\\ \int_{\mathbb{R}^{N}}|u|^2\mathrm{d}x=a^2, \end{cases} \end{equation*} where $20, a>0$ and $\lambda \in \mathbb{R}$ is a Lagrange multiplier which is unknown, $h$ is a continuous positive function and $f$ is also continuous satisfying $L^2$-subcritical growth. When $\epsilon$ is small enough, we show that the number of normalized solutions is at least the number of global maximum points of $h$ by Ekeland's variational principle. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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