Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem

• Main Authors: Yaohong Li, Zhongli Wei
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Boundary Value Problems
• Online Access: http://dx.doi.org/10.1155/2010/708376
• ISSN: 1687-2762; 1687-2770

We study the existence of multiple positive solutions for nth-order multipoint boundary value problem. u(n)(t)+a(t)f(u(t))=0, t∈(0,1), u(j-1)(0)=0(j=1,2,…,n-1), u(1)=∑i=1mαiu(ηi), where n≥2, 0<η1<η2<⋯<ηm<1, αi>0,i=1,2,…,m. We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.