Solitary waves in critical Abelian gauge theories
Emmanuel Hebey · Discrete and Continuous Dynamical Systems · 2012
We prove existence of standing waves solutionsfor electrostatic Klein-Gordon-Maxwell systems in arbitrary dimensional compact Riemannian manifoldswith 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 largephases. When $n \ge 5$, existence of a solution is obtained when the mass of the particle field is sufficiently small.