In this paper, we prove that all the positive solutions for the PDE system (-\Delta)^{ k}u_{ i} = f_{ i}(u_{ 1},..., u_{ m}), x \in R^{ n}, i = 1, 2,..., m are super polyharmonic, i.e. (-\Delta)^{ j}u_{ i} > 0, j = 1, 2,..., k - 1; i = 1, 2,...,m. To prove this important super polyharmonic property, we introduced a few new ideas and derived some new estimates. As an interesting application, we establish the equivalence between the integral system u_{ i}(x) = \int_{ R^{ n}} \frac{ 1}{ |x - y|^{ n-\alpha}}f_{ i}(u_{ 1}(y),..., u_{ m}(y))dy, x \in R^{ n} and PDE system when \alpha? = 2k < n
Categories: math.AP