On eigenvalue intervals of higher-order boundary value problems with a sign-changing nonlinear term

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摘要

In the paper, we shall consider the boundary value problem {u(n)+λa(t)f(t,u,u′,u″,u(3),…,u(n−2))=0,n≥2,t∈(0,1),u(i)(0)=0,0≤i≤n−3,αu(n−2)(0)−βu(n−1)(0)=0,γu(n−2)(1)+δu(n−1)(1)=0 where λ>0, α,β,γ and δ are constants satisfying α, γ>0 and β,δ≥0. Intervals of λ are determined to ensure the existence of a positive solution of the boundary value problem according to the signs of a(t) and f.

论文关键词:34B18,Boundary value problem,Eigenvalue,Higher-order

论文评审过程:Received 1 June 2009, Revised 12 August 2010, Available online 31 October 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.10.030