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Zbl 1183.34005
Bai, Chuanzhi
Triple positive solutions for a boundary value problem of nonlinear fractional differential equation.
(English)
[J] Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 24, 10 p., electronic only (2008). ISSN 1417-3875/e

Summary: We investigate the existence of three positive solutions for the nonlinear fractional boundary value problem $$D_{0+}^{\alpha} u(t) + a(t)f(t,u(t), u''(t))=0,\quad 0 < t < 1, \quad 3 < \alpha \leq 4,$$ $$u(0) = u'(0) = u''(0)= u''(1)=0 ,$$ where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative. The method involves applications of a new fixed-point theorem due to Bai and Ge. The interesting point lies in the fact that the nonlinear term is allowed to depend on the second order derivative $u''$.
MSC 2000:
*34A08
34B18 Positive solutions of nonlinear boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: fractional derivative; boundary value problem; positive solution; fixed point theorem

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