Positive solutions for a Kirchhoff type problem with fast increasing weight and critical nonlinearity
| Autor: | Xiaotao Qian, Wen Chao |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Electronic Journal of Qualitative Theory of Differential Equations, Vol 2019, Iss 27, Pp 1-17 (2019) |
| Druh dokumentu: | article |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2019.1.27 |
| Popis: | In this paper, we study the following Kirchhoff type problem \[ -\left(a+b\int_{\mathbb{R}^3} K(x)|\nabla u|^2dx\right)\hbox{div}(K(x)\nabla u)=\lambda K(x)|x|^{\beta}|u|^{q-2}u+K(x)|u|^{4}u,\quad x\in \mathbb{R}^3, \] where $K(x)=\exp({|x|^{\alpha}/4})$ with $\alpha\geq2$, $\beta=(\alpha-2)(6-q)/4$ and the parameters $a, b, \lambda >0$. When $6-\frac{4}{\alpha}0$. When $20$ small enough. In the proof we use variational methods. |
| Databáze: | Directory of Open Access Journals |
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