| Abstract: |
| Nonlinear curl-curl problems have recently emerged in the study of exact electromagnetic wave propagation in nonlinear media modeled by Maxwell`s equations. In particular, the quintic effect gives rise to a critical partial differential equation involving the curl-curl operator. Ground state solutions of this problem are closely related to the optimizers of a new Sobolev-type inequality. In this work, we present recent results on the existence of ground state solutions and discuss certain symmetry properties of the problem. Applications to zero modes of the Dirac equations are also considered. This is joint work with Andrzej Szulkin. |
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