Abstract
We prove that the time-independent Schrodinger polyharmonic equation (-Delta)(m) u + q (x) u = psi (x) > 0, x is an element of D, where D is an unbounded domain of R-n (n >= 2) has a positive solution provided that the function q belongs to a certain K-m,n(infinity) class of functions (D). As applications, the existence and asymptotic behavior of positive solutions of some polyharmonic problems are established.