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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/108/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |