Article ID Journal Published Year Pages File Type
4623432 Journal of Mathematical Analysis and Applications 2006 12 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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