Positive solutions for fractional differential equation with a p-Laplacian operator

• Main Authors: Yunhong LI, Yan LI
• Format: Article
• Language: zho
• Published: Hebei University of Science and Technology 2015-12-01
• Series: Journal of Hebei University of Science and Technology
• Subjects: ordinary differential equation; p-Laplacian; fractional differential equation; multi-point; positive solution; fixed point theorem
• Online Access: http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201506007&flag=1&journal_
• ISSN: 1008-1542

This paper studies the following Caputo fractional differential equation with p-Laplacian of higher-order multi-point: Dβ0+(p(Dα0+u(t)))+f(t,u(t))=0,0≤t≤1,l-1<β≤l,n-1<α≤n,(p(Dα0+u(0)))(i)=0,i=0,1,2,…,l-1,u(i)(0)=0,i=1,2,…,n-1,u(1)=∑ m-2 i=1 aiu(ξi)。 Using the Schauder fixed point theorem, the existence of positive solution is obtained for the above boundary value problems. An example is presented to illustrate our main theorem.