On a decay property of solutions to the Haraux-Weissler equation

We give a sufficient condition that non-radial H¹-solutions to the Haraux-Weissler equation should belong to the weighted Sobolev space , where ρ is the weight function exp(|x|²/4). Our result provides, in some sense, a connection between the solutions obtained by ODE method and those by variational approach in the space .