Positive solutions for a class of fractional differential equation multi-point boundary value problems with changing sign nonlinearity

摘要

In this paper, we consider the multi-point boundary value problem of nonlinear fractional differential equation $$begin{aligned} left{ begin{array}{lcl} D_{0{+}}^{alpha }u(t)+{lambda }f(t,u(t))=0, quad 00), $$begin{aligned} Delta = left{ begin{array}{ll} {1}, &{} quad {i = 0}; {(alpha - 1)(alpha - 2) cdots (alpha - i)}, &{} quad {i ge 1}. end{array} right. end{aligned}$$ (D_{0{+}}^{alpha })is the Riemann–Liouville’s fractional derivative, (f) may change sign and may be singular at (t=0,1). We give the corresponding Green’s function for the boundary value problem and its some properties. Moreover, we derive an interval of (lambda ) such that for any (lambda ) lying in this interval, the semipositone boundary value problem has positive solutions. Keywords Fractional differential equations Multi-point boundary value problem Fixed point theorem Semipositone Positive solutions Mathematics Subject Classifications 26A33 34B15 34B18 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (13) References1.Bai, Z., Lu, H.: Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005)CrossRefMATHMathSciNet2.Benchohra, M., Graef, J.R., Hamani, S.: Existence results for boundary value problems with non-linear fractional differential equations. Appl. 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Value Probl. 57, 1–9 (2012) About this Article Title Positive solutions for a class of fractional differential equation multi-point boundary value problems with changing sign nonlinearity Journal Journal of Applied Mathematics and Computing Volume 47, Issue 1-2 , pp 15-31 Cover Date2015-02 DOI 10.1007/s12190-014-0758-5 Print ISSN 1598-5865 Online ISSN 1865-2085 Publisher Springer Berlin Heidelberg Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Computational Mathematics and Numerical Analysis Appl.Mathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing Keywords Fractional differential equations Multi-point boundary value problem Fixed point theorem Semipositone Positive solutions 26A33 34B15 34B18 Industry Sectors IT & Software Telecommunications Authors Yanli Jia (1) Xingqiu Zhang (1) (2) Author Affiliations 1. School of Mathematics, Liaocheng University, Liaocheng, 252059, Shandong, People’s Republic of China 2. Department of Information Engineering, Jining Medical College, Jining, 272067, Shandong, People’s Republic of China Continue reading... To view the rest of this content please follow the download PDF link above.