Some Existence Results of Positive Solution to Second-Order Boundary Value Problems

oleh: Shuhong Li, Xiaoping Zhang, Yongping Sun

Format: Article
Diterbitkan: Hindawi Limited 2014-01-01

Deskripsi

We study the existence of positive and monotone solution to the boundary value problem u′′(t)+f(t,u(t))=0, 0⩽t⩽1, u(0)=ξu(1), u'(1)=ηu'(0), where ξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results.