Atlas: Boundary Value Problems for Nonlinear Difference Equations by Bo Yang

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Fourth Mississippi State Conference on Differential Equations and Computational Simulations
May 21-22, 1999
Mississippi State University and Electronic Journal of Differential Equations
Starkville, MS, USA

Organizers
Ratnasingham Shivaji, Bharat Soni, Jianping Zhu (Program Chair)

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Boundary Value Problems for Nonlinear Difference Equations
by
Bo Yang
Mississippi State University
Coauthors: R. Graef, Chuanxi Qian

The authors consider the nonlinear difference equation

\Delta² y_n-1+\lambda a_n f(y_n)=0, n=1, 2, ... , T-1

with the boundary conditions

y₀ = y_T = 0 or y₀ = \Delta y_T-1 = 0.

Here, T >= 2 is an integer, f:[0, \infty) --> [0, \infty) is continuous, a_n >= 0, and \lambda is a parameter. They give sufficient conditions for these problems to have a positive solution. Examples to illustrate the results and to demonstrate the sharpness of some of the hypotheses are included.

Date received: March 29, 1999