Existence of Solutions to a Third-order Multi-point Problem on Time Scales

@inproceedings{Anderson2007ExistenceOS,
  title={Existence of Solutions to a Third-order Multi-point Problem on Time Scales},
  author={Douglas R. Anderson and JOAN HOFFACKER},
  year={2007}
}
We are concerned with the existence and form of solutions to nonlinear third-order three-point and multi-point boundary-value problems on general time scales. Using the corresponding Green function, we prove the existence of at least one positive solution using the Guo-Krasnosel’skii fixed point theorem. Moreover, a third-order multi-point eigenvalue problem is formulated, and eigenvalue intervals for the existence of a positive solution are found. 

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