Infinitely many sign-changing solutions for a Schrödinger equation in RN

In this paper, we consider a Schrödinger equation −Δu+(λa(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 RN 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 RN.