Fractional elliptic equations with sign-changing and singular nonlinearity
| Autor: | Sarika Goyal, Konijeti Sreenadh |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2016, Iss 145,, Pp 1-23 (2016) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 |
| Popis: | In this article, we study the fractional Laplacian equation with singular nonlinearity $$\displaylines{ (-\Delta)^s u = a(x) u^{-q}+ \lambda b(x) u^p\quad \text{in }\Omega, \cr \quad u>0\quad \text{in }\Omega, \quad u = 0 \quad \text{in } \partial\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary $\partial \Omega$, $n> 2s$, $s\in(0,1)$, $\lambda>0$. Using variational methods, we show existence and multiplicity of positive solutions. |
| Databáze: | Directory of Open Access Journals |
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