Unbounded solutions of second order discrete BVPs on infinite intervals

Abstract

In this paper, we study Sturm-Liouville boundary value problems for second order difference equations on a half line. By using the discrete upper and lower solutions, the Schäuder fixed point theorem, and the degree theory, the existence of one and three solutions are investigated. An interesting feature of our existence theory is that the solutions may be unbounded.

The Solvability of the Discrete Boundary Value Problem on the Half-Line

“…More information about properties of Fredholm operators can be found in [13,15,16] and the references therein. Many authors have considered a discrete version of (1) or its generalizations using different tools, see for example [2,[17][18][19][20][21] and the references therein. Lian et al,in [19], established the sufficient conditions for the existence of one and three solutions of the following problem:…”

Solvability of second-order m-point difference equation boundary value problems on infinite intervals

“…In [15], Lian et al used the Schauder fixed point theorem and upper and lower solution technique to study unbounded positive solutions for second-order discrete boundary value problems on infinite intervals…”