Two-point right focal eigenvalue problems on time scales

摘要

We consider the following right focal boundary value problem:(-1)n-1yΔn(t)=λ(-1)p+1F(t,y(σn-1(t))),t∈[a,b]∩T,yΔi(a)=0,0⩽i⩽p-1yΔi(σ(b))=0,p⩽i⩽n-1where λ > 0, n ⩾ 2, 1 ⩽ p ⩽ n − 1 is fixed and T is a time scale. The Green’s function related to the boundary value problem is obtained. The values of λ are characterized so that this problem has a positive solution. In addition, explicit intervals of λ are established. We also include examples to illustrate the usefulness of the results obtained.