Existence Of Positive Solutions Of Boundary Value Prolems For Third Order Difference Systems

This paper is concerned with the following systemâ–³³u_i(k) + f_i(k, U₁(k),u₂(k),..., u_n(k)) = 0, k ∈ [0, T], i = 1,2,..., n, with the Dirichlet boundary conditionu_i(0) = u_i(1) = u_i(T + 3) = 0, i = 1, 2,.... n.Some results are obtained for the existence, multiplicity and nonexistence of positive solutions to the above system by using nonlinear alternative of Leray-Schauder type, Krasnosel'skii's fixed point theorem in a cone and Leggett-Williams fixed point theorem. In particular, it prove that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer.