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

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.