EXISTENCE OF POSITIVE SOLUTIONS FOR BVPS TO INFINITE DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

Motivated by Agarwal and O Regan ( Boundary value problems for general discrete systems on in¯nite intervals, Comput. Math. Appl. 33(1997)85-99), this article deals with the discrete type BVP of the in¯nite di？？erence equations. The su±cient condi-tions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main re- sults. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multi-¯xed-point theorems can be extended to treat BVPs for in¯nite di？？erence equations. The strong Caratheodory (S-Caratheodory) function is de¯ned in this paper.