SOLUTIONS OF NONLINEAR PERIODIC DIRAC EQUATIONS WITH PERIODIC POTENTIALS

摘要

This paper is concerned with the nonlinear Dirac equation -i∑~3_(k=1) α_k∂_ku + [V (ⅹ) + a]βu + ωu = f(x, u) in R~3, where V (ⅹ) and f(x, u) are periodic in x, f(x, u) is asymptotically linear and superlinear as |u| → ∞. Under weaker assumptions on f, we obtain the existence of one nontrivial solution for the above equation.