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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.

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