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Existence of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

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2 Author(s)
Hong-Ling Lu ; Sch. of Math., Univ. of Jinan, Jinan, China ; Zhen-Lai Han

In this paper, we investigate the existence of positive solutions of fractional differential equations with p-Laplacian operator: D0+γp(D0+αu(t)))=f(t,u(t)), 0<;t<;1,u(0) = u'(0)=u'(1)=0, D0+αu(0) = D0+αu'(1) = 0, 1<;γ≤2, 2<;α≤3, φp(s)=|s|p-2 s, p >; 1, where (φp)-1= φq, 1/p + 1/q= 1 and D0+α, D0+γ is the standard Riemann-Liouville differentiation. It is valuable to point out that the nonlinearity f can be singular at t = 0, 1 or u= 0. By the use of fixed point theorem on cone and the upper and lower solutions method, the existence of positive solutions is obtained.

Published in:

Computer Science and Information Processing (CSIP), 2012 International Conference on

Date of Conference:

24-26 Aug. 2012