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

Marino Badiale; Vieri Benci; Sergio Rolando

Journal of the European Mathematical Society (2007)

- Volume: 009, Issue: 3, page 355-381
- ISSN: 1435-9855

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topBadiale, 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 -

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