Multiple solutions for a class of nonperiodic Dirac equations with vector potentials

This paper is concerned with the nonperiodic Dirac equations {−i∑k=13αk∂ku+aβu+M(x)u=Fu(x,u)inR3,u(x)→0as|x|→∞, where M(x)M(x) is a vector potential. We introduce a new assumption on the potential MM, and prove that the corresponding Dirac operator has only a point spectrum. Moreover, by applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity.