Superlinear singular fractional boundary-value problems
In this article, we study the superlinear fractional boundary-value problem $$\displaylines{ D^{\alpha }u(x) =u(x)g(x,u(x)),\quad 0<x<1, \cr u(0)=0,\quad \lim_{x\to0^{+}} D^{\alpha -3}u(x)=0,\cr \lim_{x\to0^{+}} D^{\alpha -2}u(x)=\xi ,\quad u''(1)=\zeta , }$$ where $3<\alp...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-04-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/108/abstr.html |
| _version_ | 1828845527930765312 |
|---|---|
| author | Imed Bachar Habib Maagli |
| author_facet | Imed Bachar Habib Maagli |
| author_sort | Imed Bachar |
| collection | DOAJ |
| description | In this article, we study the superlinear fractional
boundary-value problem
$$\displaylines{
D^{\alpha }u(x) =u(x)g(x,u(x)),\quad 0<x<1, \cr
u(0)=0,\quad \lim_{x\to0^{+}} D^{\alpha -3}u(x)=0,\cr
\lim_{x\to0^{+}} D^{\alpha -2}u(x)=\xi ,\quad u''(1)=\zeta ,
}$$
where $3<\alpha \leq 4$, $D^{\alpha }$ is the Riemann-Liouville
fractional derivative and $\xi ,\zeta \geq 0$ are such that $\xi +\zeta >0$.
The function $g(x,u)\in C((0,1)\times [ 0,\infty ),[0,\infty))$
that may be singular at x=0 and x=1 is required to satisfy
convenient hypotheses to be stated later. |
| first_indexed | 2024-12-12T21:30:13Z |
| format | Article |
| id | doaj.art-1750b139a91443aca6a34e6d619b2e03 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T21:30:13Z |
| publishDate | 2016-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1750b139a91443aca6a34e6d619b2e032022-12-22T00:11:21ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-04-012016108,115Superlinear singular fractional boundary-value problemsImed Bachar0Habib Maagli1 King Saud Univ., Riyadh, Saudi Arabia King Saud Univ., Riyadh, Saudi Arabia In this article, we study the superlinear fractional boundary-value problem $$\displaylines{ D^{\alpha }u(x) =u(x)g(x,u(x)),\quad 0<x<1, \cr u(0)=0,\quad \lim_{x\to0^{+}} D^{\alpha -3}u(x)=0,\cr \lim_{x\to0^{+}} D^{\alpha -2}u(x)=\xi ,\quad u''(1)=\zeta , }$$ where $3<\alpha \leq 4$, $D^{\alpha }$ is the Riemann-Liouville fractional derivative and $\xi ,\zeta \geq 0$ are such that $\xi +\zeta >0$. The function $g(x,u)\in C((0,1)\times [ 0,\infty ),[0,\infty))$ that may be singular at x=0 and x=1 is required to satisfy convenient hypotheses to be stated later.http://ejde.math.txstate.edu/Volumes/2016/108/abstr.htmlFractional differential equationpositive solutionGreen's functionperturbation arguments |
| spellingShingle | Imed Bachar Habib Maagli Superlinear singular fractional boundary-value problems Electronic Journal of Differential Equations Fractional differential equation positive solution Green's function perturbation arguments |
| title | Superlinear singular fractional boundary-value problems |
| title_full | Superlinear singular fractional boundary-value problems |
| title_fullStr | Superlinear singular fractional boundary-value problems |
| title_full_unstemmed | Superlinear singular fractional boundary-value problems |
| title_short | Superlinear singular fractional boundary-value problems |
| title_sort | superlinear singular fractional boundary value problems |
| topic | Fractional differential equation positive solution Green's function perturbation arguments |
| url | http://ejde.math.txstate.edu/Volumes/2016/108/abstr.html |
| work_keys_str_mv | AT imedbachar superlinearsingularfractionalboundaryvalueproblems AT habibmaagli superlinearsingularfractionalboundaryvalueproblems |