On the existence of radial positive entire solutions for polyharmonic systems

Two-dimensional nonlinear, polyharmonic systems of the type nuj (pj−2) nuj = fj |x|,u1,u2, |∇u1|, |∇u2| , x∈ R2, j = 1, 2, are considered, where pj > 1 is a constant and fj : [0,∞) × (0,∞)2 × [0,∞)2 →[0,∞) is a continuous function for j = 1, 2. Some sufficient conditions are obtained for the existence of infinitely many radial positive entire solutions of the system with the prescribed asymptotic behavior at infinity. © 2006 Elsevier Inc. All rights reserved