MULTIPLE POSITIVE SOLUTIONS FOR DYNAMIC m-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider a second order m-point boundary value problem for dynamic equations on time scales. First, we establish criteria for the existence of one or more than one positive solution of a non-eigenvalue problem. Second, we consider the existence and multiplicity of positive solutions for an eigenvalue problem. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use fixed point theorems for operators on a Banach space.