On strongly increasing entire solutions of even order semilinear elliptic equations (Q1096078)

This paper is devoted to the question of existence and nonexistence of radial entire solutions of even order semilinear elliptic equations \[ \Delta^ mu=f(| x|,u,\Delta u,...,\Delta^{m-1}u)\quad on\quad {\mathbb{R}}^ n \] which are strongly increasing in the sense of \[ | u(x)| | x|^{2-2m}\to \infty \quad for\quad | x| \to \infty,\;if\;n\geq 3 \] (and an additional log\(| x|\)-term in case of \(n=2)\). The results are established on the basis of some criteria given by Kusano, Naito, and Swanson. Further it is shown that in the second order case \((m=1)\) the results can be transposed to the nonradial case via sub- and supersolution-technique.