Nodal Solutions For A Generalized Quasilinear Schrodinger Equation With Critical Nonlinearity

This paper is concerned with the existence of nodal solutions for a generalized quasilinear Schrodinger equations-div(g2(u)â–½u)+g(u)g’(u)|â–½u|2+V(x)u= k(u), where x(?) RN, N≥3, g:Râ†'R+ is an even differential function and g’(s)≥ 0 for all s≥ 0, k:Râ†' R is a continuous function, the potential V(x):RN â†' R is positive in RN.For any given integer k≥ 0, by using a change of variables and Nehari minimization, we proved the equations above exist a sign-changing solution with k nodes.