%0 Journal Article %J J. Eur. Math. Soc. 7 (2005) 117-144 %D 2005 %T Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity %A Antonio Ambrosetti %A Veronica Felli %A Andrea Malchiodi %X We deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$. %B J. Eur. Math. Soc. 7 (2005) 117-144 %G en_US %U http://hdl.handle.net/1963/2352 %1 1664 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-07T08:16:53Z\\nNo. of bitstreams: 1\\nGround states.pdf: 901500 bytes, checksum: 741c3d55677b872a40e8e3ff2df2a5d2 (MD5)