Infinite multiplicity for an inhomogeneous supercritical problem in entire space
Baishun Lai, Zhihao Ge · Proceedings of the American Mathematical Society · 2011
In this paper, we will prove the existence of infinitely many positive solutions to the following supercritical problem by using the Liapunov-Schmidt reduction method and asymptotic analysis: { Δ u + u p + f ( x ) = 0 , u > 0 in R n , lim | x | → ∞ u ( x ) → 0. \begin{eqnarray*} \left \{ \begin {array}{ll} \Delta u + u^{p}+f(x)=0,\ \ u>0\ \ \mbox {in}\ \mathbb {R}^{n},\\ \lim _{|x|\to \infty }u(x)\to 0. \end{array} \right . \end{eqnarray*}