| Title | Ground states of nonlinear Schroedinger equations with potentials vanishing at infinity |
| Publication Type | Journal Article |
| Year of Publication | 2005 |
| Authors | Ambrosetti, A, Felli, V, Malchiodi, A |
| Journal | J. Eur. Math. Soc. 7 (2005) 117-144 |
| Abstract | 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 $\\\\theta= (p+1)/(p-1)-1/2$. |
| URL | http://hdl.handle.net/1963/2352 |
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