A nonlinear elliptic equation with singular potential and applications to nonlinear field equations

Badiale, Marino, Benci, Vieri, and Rolando, Sergio. "A nonlinear elliptic equation with singular potential and applications to nonlinear field equations." Journal of the European Mathematical Society 009.3 (2007): 355-381. <http://eudml.org/doc/277178>.

@article{Badiale2007,
abstract = {We prove the existence of cylindrical solutions to the semilinear elliptic problem $−\Delta u+\frac\{u\}\{|y|^2\}=f(u)$, $u\in H^1(\mathbb \{R\}^N)$, $u\ge 0$, where $(y,z)\in \mathbb \{R\}^k\times \mathbb \{R\}^\{N−k\}$, $N>k\ge 2$ and $f$ has a double-power behaviour, subcritical at infinity and supercritical near the origin. This result also implies the existence of solitary waves with nonvanishing angular momentum for nonlinear Schr¨odinger and Klein–Gordon equations.},
author = {Badiale, Marino, Benci, Vieri, Rolando, Sergio},
journal = {Journal of the European Mathematical Society},
keywords = {semilinear elliptic equation; singular potential; asymptotic behavior; solitary wave; semilinear elliptic equation; nonlinear fields equation; solitary waves; Schrödinger equation; Klein-Gordon equation},
language = {eng},
number = {3},
pages = {355-381},
publisher = {European Mathematical Society Publishing House},
title = {A nonlinear elliptic equation with singular potential and applications to nonlinear field equations},
url = {http://eudml.org/doc/277178},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Badiale, Marino
AU - Benci, Vieri
AU - Rolando, Sergio
TI - A nonlinear elliptic equation with singular potential and applications to nonlinear field equations
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 3
SP - 355
EP - 381
AB - We prove the existence of cylindrical solutions to the semilinear elliptic problem $−\Delta u+\frac{u}{|y|^2}=f(u)$, $u\in H^1(\mathbb {R}^N)$, $u\ge 0$, where $(y,z)\in \mathbb {R}^k\times \mathbb {R}^{N−k}$, $N>k\ge 2$ and $f$ has a double-power behaviour, subcritical at infinity and supercritical near the origin. This result also implies the existence of solitary waves with nonvanishing angular momentum for nonlinear Schr¨odinger and Klein–Gordon equations.
LA - eng
KW - semilinear elliptic equation; singular potential; asymptotic behavior; solitary wave; semilinear elliptic equation; nonlinear fields equation; solitary waves; Schrödinger equation; Klein-Gordon equation
UR - http://eudml.org/doc/277178
ER -