EXISTENCE RESULTS FOR POSITIVE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721–732], this article deals with the following discrete type BVP    ∆[φ(∆x(n))] + f(n, x(n + 1), ∆x(n), ∆x(n + 1)) = 0, n ∈ [0, N ], x(0)−mi=1 αix(ni) = A, x(N + 2)−mi=1 βix(ni) = B. The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ∆x(n).