Least Energy Nodal Solutions for a Defocusing Schrödinger Equation with Supercritical Exponent

In this paper we consider the existence of least energy nodal solution for the defocusing quasilinear Schrödinger equation $$-\Delta u - u \Delta u^2 + V(x)u = a(x)[g(u) + \lambda \vert u \vert ^{p-2}u] \hbox{in} {\open R}^N,$$ where λ≥0 is a real parameter, V(x) is a non-vanishing function, a(x) can be a vanishing positive function at infinity, the nonlinearity g(u) is of subcritical growth, the exponent p≥22*, and N≥3. The proof is based on a dual argument on Nehari manifold by employing a deformation argument and an $L</italic>^{\infty}({\open R}^{N})$-estimative.