“…This equation and its extensions have been involved in many models of mathematical physics and received considerable attention during the last years, we refer [5,9,13,14,18,30,31,32] and the references therein. When 4 ≤ r < 4N N −2 , existence theory and multiple solutions for (MNSE) and the general equation (1.1) have been well developed in recent years, see [8,11,19,27,28,26,22,23]. Multiple sign-changing solutions of positive energies have been obtained for the quasilinear equation (1.1), c.f., [19].…”