Positive entire solutions of higher order semilinear elliptic equations (Q1119821)

The author proves the existence of positive radial \(C^{2n}\)-solutions for \[ (\Delta -a^ 2_ 1)^{p_ 1}...(\Delta -a^ 2_ m)^{p_ m} u=f(| x|,u) \] on \(R^{\ell}\), where \(0<a_ 1<a_ 2<...<a_ m\), \(p_ i\in {\mathbb{N}}\) for \(1<i<m\), and \(n=p_ 1+...+p_ m.\) f is supposed to be continuous and \(| f|\) is majorized by a function \(f^*\), which is e.g. superlinear at 0 or sublinear at \(\infty.\) Informations about the asymptotic behavior of those solutions are also obtained.