In this paper, we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to honeycomb structures. Such equation is critical for the Sobolev embedding and solutions are found by variational methods. Moreover, we also prove smoothness and exponential decay at infinity.

Symmetric Solutions for a 2D Critical Dirac Equation

William Borrelli
2021-01-01

Abstract

In this paper, we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to honeycomb structures. Such equation is critical for the Sobolev embedding and solutions are found by variational methods. Moreover, we also prove smoothness and exponential decay at infinity.
2021
Nonlinear Dirac equations
critical point theory
existence results
critical nonlinearity
honeycomb structure
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1221307
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