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: { -Delta u + V (x)u - (2 omega + phi)phi u = f(x, u), x is an element of R-3, Delta phi = (omega + phi)u(2), x is an element of R-3, where omega > 0 is a constant, V is an element of C(R-3, R),f is an element of C(R-3 x 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. (C) 2018 Elsevier Ltd. All rights reserved.