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Two-point right focal eigenvalue problems on time scales. (English) Zbl 1084.39018

The authors consider the right focal boundary value problem

(-1) n-1 y Δ n (t)=λ(-1) p+1 F(t,y(σ n-1 (t))),t[a,b]T,
y Δ i (a)=0,0ip-1,y Δ i (σ(b))=0,pin-1,

where λ>0, n2, 1pn-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. The paper also contents examples to illustrate the usefulness of the results obtained.

MSC:
39A12Discrete version of topics in analysis
34L05General spectral theory for OD operators
39A11Stability of difference equations (MSC2000)