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Multiplicity of solutions for asymptotically quadratic Dirac-Poisson system with non-periodic potential. (English) Zbl 1475.35008

Summary: In this paper we study a class of Dirac-Poisson system with non-periodic potential. The Dirac operator is unbounded from below and above, so the associated energy functional is strongly indefinite. By using linking theorem for strongly indefinite functionals, we obtain a new multiplicity result of solutions when the nonlinearity has asymptotic quadratic growth.

MSC:

35A15 Variational methods applied to PDEs
35J61 Semilinear elliptic equations
35Q41 Time-dependent Schrödinger equations and Dirac equations
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