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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 $$(-1)^{n-1}y^{\Delta ^{n}}(t)=\lambda (-1)^{p+1}F(t,y(\sigma ^{n-1}(t))),\quad t\in [a,b]\cap T,$$ $$y^{\Delta ^{i}}(a)=0,\quad 0\leq i\leq p-1,\quad y^{\Delta ^{i}}(\sigma (b))=0,\quad p\leq i\leq n-1,$$ where $\lambda >0,$ $n\geq 2,$ $1\leq p\leq n-1$ is fixed and $T$ is a time scale. The Green’s function related to the boundary value problem is obtained. The values of $\lambda $ are characterized so that this problem has a positive solution. In addition, explicit intervals of $\lambda $ are established. The paper also contents examples to illustrate the usefulness of the results obtained.

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