Existence of positive solutions for Kirchhoff problems
| Autor: | Jia-Feng Liao, Peng Zhang, Xing-Ping Wu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2015, Iss 280,, Pp 1-12 (2015) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 |
| Popis: | We study problems for the Kirchhoff equation $$\displaylines{ -\Big(a+b\int_{\Omega}|\nabla u|^2dx\Big)\Delta u =\nu u^3+ Q(x)u^{q},\quad \text{in }\Omega, \cr u=0, \quad \text{on }\partial\Omega, }$$ where $\Omega\subset \mathbb{R}^3$ is a bounded domain, $a,b\geq0$ and $a+b>0$, $\nu>0$, $30$ in $\Omega$. By the mountain pass lemma, the existence of positive solutions is obtained. Particularly, we give a condition of Q to ensure the existence of solutions for the case of q=5. |
| Databáze: | Directory of Open Access Journals |
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