Eigenvalues of Lidstone boundary value problems

摘要

We consider the following boundary value problem: (−1)ny(2n)=λF(t,y),n⩾1,t∈(0,1), y(2i)(0)=y(2i)(1)=0,0⩽i⩽n−1, where λ>0. The values of λ are characterized so that the boundary value problem has a positive solution. In addition, we derive explicit intervals of λ such that for any λ in the interval, existence of a positive solution of the boundary value problem is guaranteed. Several examples are also included to dwell upon the importance of the results obtained.