Abstract
In this chapter, the Maxwell equations are deduced from the general principles of Chap. 1. If these equations are coupled with the nonlinear Klein-Gordon equation, we get the simplest gauge theory with “matter”. After having analyzed the general features of these equations, we apply the abstract theory of Chap. 2 and we prove the existence of hylomorphic solitons.
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Notes
- 1.
\(\mathcal{D}^{1,2}\) is the closure of C 0 ∞ with respect to the norm \(\left \Vert \nabla \varphi \right \Vert _{L^{2}}\).
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Benci, V., Fortunato, D. (2014). The Nonlinear Klein-Gordon-Maxwell Equations. In: Variational Methods in Nonlinear Field Equations. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06914-2_5
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DOI: https://doi.org/10.1007/978-3-319-06914-2_5
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