Prior Estimates and Solutions of Boundary Value Problems for Higher-Order Nonlinear Finite Difference Equations

  • Liu, Yuji (Department of Mathematics, Guangdong University of Business Studies)
  • Received : 2006.06.01
  • Published : 2007.12.23

Abstract

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

Keywords

References

  1. R. P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations, Kluwer, Dordrecht, 1998.
  2. R. P. Agarwal, D. O'Regan and P. J. Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999.
  3. L. Kong, Q. Kong and B. Zhang, Positive solutins of boundary value problems for third order functional difference equations, Comput. Math. with Applications, 44(2002), 481-489. https://doi.org/10.1016/S0898-1221(02)00170-0
  4. R. P. Agarwal and J. Henderson, Positive solutions and nonlinear eigenvalue problems for third order difference equations, Comput. Math. with Applications, 36(1998), 347- 355. https://doi.org/10.1016/S0898-1221(98)80035-7
  5. J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations, in: P. M. Fitzpertrick, M. Martelli, J. Mawhin, R. Nussbanm(Eds.), Topological Methods for Ordinary Differential Equations, Lecture Notes in Math. Springer- Verlag, New York/Berlin, 1537(1991).