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2012 Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives
Tunhua Wu, Xinguang Zhang, Yinan Lu
Abstr. Appl. Anal. 2012(SI11): 1-16 (2012). DOI: 10.1155/2012/797398


We study the singular fractional-order boundary-value problem with a sign-changing nonlinear term -𝒟αx(t)=p(t)f(t,x(t),𝒟μ1x(t),𝒟μ2x(t),,𝒟μn-1x(t)),0<t<1,𝒟μix(0)=0,1in-1,𝒟μn-1+1x(0)=0, 𝒟μn-1x(1)=j=1p-2aj𝒟μn-1x(ξj), where n-1<αn, n and n3 with 0<μ1<μ2<<μn-2<μn-1 and n-3<μn-1<α-2, aj,0<ξ1<ξ2<<ξp-2<1 satisfying 0<j=1p-2ajξjα-μn-1-1<1, 𝒟α is the standard Riemann-Liouville derivative, f:[0,1]×n is a sign-changing continuous function and may be unbounded from below with respect to xi, and p:(0,1)[0,) is continuous. Some new results on the existence of nontrivial solutions for the above problem are obtained by computing the topological degree of a completely continuous field.


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Tunhua Wu. Xinguang Zhang. Yinan Lu. "Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives." Abstr. Appl. Anal. 2012 (SI11) 1 - 16, 2012.


Published: 2012
First available in Project Euclid: 4 April 2013

zbMATH: 1253.35206
MathSciNet: MR2969981
Digital Object Identifier: 10.1155/2012/797398

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI11 • 2012
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