Differential and Integral Equations

Multiplicity for a nonlinear fourth-order elliptic equation in Maxwell-Chern-Simons vortex theory

Tonia Ricciardi

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Abstract

We prove the existence of at least two solutions for a fourth-order equation, which includes the vortex equations for the $U(1)$ and $CP(1)$ self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an ``asymptotic maximum principle" property for a special class of supersolutions to this fourth-order equation.

Article information

Source
Differential Integral Equations Volume 17, Number 3-4 (2004), 369-390.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060437

Mathematical Reviews number (MathSciNet)
MR2037982

Zentralblatt MATH identifier
1174.35375

Subjects
Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]
Secondary: 35J60: Nonlinear elliptic equations 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Ricciardi, Tonia. Multiplicity for a nonlinear fourth-order elliptic equation in Maxwell-Chern-Simons vortex theory. Differential Integral Equations 17 (2004), no. 3-4, 369--390. https://projecteuclid.org/euclid.die/1356060437.


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