Existence and asymptotic behavior of positive solutions for semilinear fractional Navier boundary-value problems
| Autor: | Habib Maagli, Abdelwaheb Dhifli |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2017, Iss 141,, Pp 1-13 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 94959048 |
| Popis: | We study the existence, uniqueness, and asymptotic behavior of positive continuous solutions to the fractional Navier boundary-value problem $$\displaylines{ D^{\beta }(D^{\alpha }u)(x)=-p(x)u^{\sigma },\quad \in (0,1), \cr \lim_{x\to 0}x^{1-\beta }D^{\alpha}u(x)=0,\quad u(1)=0, }$$ where $\alpha ,\beta \in (0,1]$ such that $\alpha +\beta >1$, $D^{\beta }$ and $D^{\alpha }$ stand for the standard Riemann-Liouville fractional derivatives, $\sigma \in (-1,1)$ and p being a nonnegative continuous function in (0,1) that may be singular at x=0 and satisfies some conditions related to the Karamata regular variation theory. Our approach is based on the Schauder fixed point theorem. |
| Databáze: | Directory of Open Access Journals |
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