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Existence and nonexistence of positive solutions for a nonlinear fractional boundary value problem
| 1. | Department of Mathematics & Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, United States |
- Abstract
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$\D_0^\alpha + u(t) + f(t, u(t)) = 0,$ $t \in (0, \tau),$
$I^\gamma u(0^+) = 0,$ $I^\beta u(\tau) = 0,$
where $1 - \alpha < \gamma \leq 2 - \alpha,$ $2 - \alpha < \beta < 0$, $\D_(0+)^\alpha$ is the Riemann-Liouville differential operator of order $\alpha $, and $f \in C([0,T] \times \mathbb{R})$ is nonnegative, has a positive solution. We also present a nonexistence result.
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