On the existence of radial positive entire solutions for polyharmonic systems

Two-dimensional nonlinear, polyharmonic systems of the typeΔ(|Δnuj|(pj−2)Δnuj)=fj(|x|,u1,u2,|∇u1|,|∇u2|),x∈R2,j=1,2, are considered, where pj>1pj>1 is a constant and fj:[0,∞)×(0,∞)2×[0,∞)2→[0,∞) is a continuous function for j=1,2j=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.