Infinitely many solutions and least energy solutions for Klein-Gordon-Maxwell systems with general superlinear nonlinearity

This paper is concerned with the following Klein-Gordon-Maxwell system: −△u+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,△ϕ=(ω+ϕ)u2,x∈R3,where ω>0 is a constant, V∈C(R3,R), f∈C(R3×R,R), and f is superlinear at infinity. Using some weaker superlinear conditions instead of the common super-cubic conditions on f, we prove that the above system has (1) infinitely many solutions when V(x) is coercive and sign-changing; (2) a least energy solution when V(x) is positive periodic. These results improve the related ones in the literature.