Infinitely many sign-changing solutions for a Schrِdinger equation in

In this paper, we consider a Schrödinger equation − Δ u + ( λ a ( x ) + 1 ) u = f ( u ) . Applying Principle of Symmetric Criticality and the invariant set method, under some assumptions on a and f, we obtain an unbounded sequence of radial sign-changing solutions for the above equation in R N when λ > 0 large enough. As N = 4 or N ⩾ 6 , λ > 0 given, using Fountain Theorem and the Principle of Symmetric Criticality, we prove that there exists an unbounded sequence of non-radial sign-changing solutions for the above equation in R N .