ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION

This paper is concerned with existence and concentration phenomena of semiclassical solutions of the following nonlinear Dirac equation [Formula: see text] for x ∈ ℝ 3 where p j ∈ (2, 3) are subcritical. Under some conditions, we show that there are two families of semiclassical solutions, for ℏ > 0 small, with the least energy, one concentrating on the set of minimal points of V and another on the set of maximal points of W j . Both are exponentially decay as |x| → ∞.