Multiple solutions for a class of semilinear elliptic equations with general potentials

In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations −△u+a(x)u=g(x,u)−△u+a(x)u=g(x,u) in a bounded smooth domain of RN(N≥3)RN(N≥3) with the Dirichlet boundary value, where the primitive of the nonlinearity gg is of superquadratic growth near infinity in uu and the potential aa is allowed to be sign-changing. Recent results in the literature are generalized and significantly improved.