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The nonnegative solution for fractional boundary value problem at resonance
Qu Haidong 1,Liu Xuan 2 *
1.Department of Mathematics, Hanshan normal University, GuangDong ChaoZhou 521041
2.Department of Basic Education, Hanshan normal University, GuangDong ChaoZhou 521041
*Correspondence author
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Funding: none
Opened online: 8 June 2012
Accepted by: none
Citation: Qu Haidong,Liu Xuan.The nonnegative solution for fractional boundary value problem at resonance[OL]. [ 8 June 2012] http://en.paper.edu.cn/en_releasepaper/content/4480637
 
 
This article is devoted to the study of the non-negative solutions to boundary valueproblem for nonlinear fractional differential equation, and the parameters in theequation are such that the boundary value problem is at resonance. First, the fractional boundary value problem is transformed into the operator equation, and the kernel set image set of the operator are calculated. Then two consecutive adjoint operator is defined according to the definition of the operator and the boundary conditions, and the non-negative solutions of boundary value problem at resonance are obtained by using the extended upper and lower solution theorem. Finally, an detailed example is given to demonstrate the main result.
Keywords:Fractional differential equation; Boundary value problem; At resonance; Cone; Coincidence degree
 
 
 

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