Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623432 | Journal of Mathematical Analysis and Applications | 2006 | 12 Pages |
Abstract
In this paper, by using Krasnosel'skii fixed point theorem and under suitable conditions, we present the existence of single and multiple positive solutions to the following systems:{(−1)pu(2p)=λa(t)f(u(t),v(t)),t∈[0,1],(−1)qv(2q)=μb(t)g(u(t),v(t)),t∈[0,1],u(2i)(0)=u(2i)(1)=0,0⩽i⩽p−1,v(2j)(0)=v(2j)(1)=0,0⩽j⩽q−1, where λ>0λ>0, μ>0μ>0, p,q∈Np,q∈N. We derive two explicit intervals of λ and μ such that for any λ and μ in the two intervals respectively, the existence of at least one solution to the systems is guaranteed, and the existence of at least two solutions for λ and μ in appropriate intervals is also discussed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yuanfang Ru, Yukun An,