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

  title={Existence of Solutions to a Third-order Multi-point Problem on Time Scales},
  author={Douglas R. Anderson and JOAN HOFFACKER},
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. 

From This Paper

Topics from this paper.
2 Citations
18 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 18 references

Nonlinear Problems in Abstract Cones

  • D. Guo, V. Lakshmikantham
  • Academic Press, San Diego
  • 1988
Highly Influential
5 Excerpts

Positive solutions of a singular nonlinear third-order two-point boundary value problem

  • Z. Q. Liu, J. S. Ume, S. M. Kang
  • J. Math. Anal. Appl., 326
  • 2007
3 Excerpts

Positive solutions to a singular third-order 3-point boundary value problem with indefinitely signed Green’s function

  • A. P. Palamides, G. Smyrlis
  • Nonliner Anal.,
  • 2007

Third-order boundary value problems with sign-changing solutions

  • B. Hopkins, N. Kosmatov
  • Nonlinear Anal., 67:1
  • 2007
2 Excerpts

Similar Papers

Loading similar papers…