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Solitary waves in critical Abelian gauge theories

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  • We prove existence of standing waves solutions for electrostatic Klein-Gordon-Maxwell systems in arbitrary dimensional compact Riemannian manifolds with boundary for zero Dirichlet boundary conditions. We prove that phase compensation holds true when the dimension $n = 3$ or $4$. In these dimensions, existence of a solution is obtained when the mass of the particle field, balanced by the phase, is small in a geometrically quantified sense. In particular, existence holds true for sufficiently large phases. When $n \ge 5$, existence of a solution is obtained when the mass of the particle field is sufficiently small.
    Mathematics Subject Classification: Primary: 35J62, 35J47; Secondary: 35J20.


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