Opuscula Math. 30, no. 4 (2010), 447-456
http://dx.doi.org/10.7494/OpMath.2010.30.4.447
Opuscula Mathematica
Right focal boundary value problems for difference equations
Johnny Henderson
Xueyan Liu
Jeffrey W. Lyons
Jeffrey T. Neugebauer
Abstract. An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.
Keywords: difference equation, boundary value problem, right focal, fixed point theorem, positive solution.
Mathematics Subject Classification: 39A10.
- Johnny Henderson
- Baylor University, Department of Mathematics, Waco, Texas 76798-7328 USA
- Xueyan Liu
- Baylor University, Department of Mathematics, Waco, Texas 76798-7328 USA
- Jeffrey W. Lyons
- Baylor University, Department of Mathematics, Waco, Texas 76798-7328 USA
- Jeffrey T. Neugebauer
- Baylor University, Department of Mathematics, Waco, Texas 76798-7328 USA
- Received: 2010-04-21.
- Accepted: 2010-05-11.
