A nonradial bifurcation result with applications to supercritical problems (Q269418)

Let \(\alpha\) be a positive number. This paper is concerned with the bifurcation analysis of positive solutions decaying to zero at infinity of the semilinear elliptic equation \(-\Delta u=|x|^\alpha F(u)\) in \({\mathbb R}^N\) (\(N\geq 3\)), where \(F\) is a smooth function. Under some natural hypotheses, the authors establish the existence of nonradial solutions that bifurcate from the radial one, provided that \(\alpha\) is an even integer number. The proof combines techniques of nonlinear differential equations with elements of Morse theory.