Third-order Nonlocal Problems with Sign-changing Nonlinearity on Time Scales

  title={Third-order Nonlocal Problems with Sign-changing Nonlinearity on Time Scales},
  author={Douglas R. Anderson and Christopher C. Tisdell},
We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green’s functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to change sign in our formulation, and the novelty of the boundary conditions, these results are new for discrete, continuous, quantum and arbitrary time… CONTINUE READING

From This Paper

Topics from this paper.
5 Citations
27 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 27 references

Nonlinear Problems in Abstract Cones

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

Multiple solutions to dynamic equations on time scales

  • C. C. Tisdell, P. Drábek, J. Henderson
  • Comm. Appl. Nonlinear Anal. 11:4
  • 2004
Highly Influential
8 Excerpts

Double solutions of impulsive dynamic boundary value problems on a time scale

  • J. Henderson
  • J. Diff. Equations Appl., 8:4
  • 2002
Highly Influential
8 Excerpts

Multiplicity of positive solutions for higher order Sturm-Liouville problems

  • J. M. Davis, L. H. Erbe, J. Henderson
  • Rocky Mountain J. Math., 31
  • 2001
Highly Influential
7 Excerpts

Multiple solutions for 2mth order Sturm-Liouville boundary value problems on a measure chain

  • J. Henderson
  • J. Differ. Equations Appl., 6
  • 2000
Highly Influential
7 Excerpts

Eigenvalue characterization for a system of third-order generalized right focal problems

  • P.J.Y. Wong
  • Dynamic Sys. Appl., 15
  • 2006
2 Excerpts

Similar Papers

Loading similar papers…