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 {Delta[phi(Delta x(n))] + f(n,x(n + 1), Delta x(n), Delta x(n + 1)) = 0, n is an element of [0, N], x(0) - Sigma(m)(i=1) alpha(i)x(n(i)) = A, x(N + 2) - Sigma(m)(i=1) beta(i)x(n(i)) = 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 Delta x(n).