Concentration of Semi-Classical States for Nonlinear Dirac Equations of Space-Dimension n
Keywords:
Dirac equations, semi-classical states, concentration.Abstract
In the present paper, we study the semi-classical approximation of a massive Dirac equation in space-dimension n ≥ 2 with some general nonlinear self-coupling. We prove that there exists a family of ground states of the semi-classical problem, for all ~ small, and show that the family concentrates around some certain sets determined by the competing potential functions as ~ → 0.
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