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

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

2003-02-05

arxiv.org/abs/math/0302051v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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.

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