INFINITELY MANY SIGN-CHANGING SOLUTIONS FORQUASILINEAR SCHRODINGER EQUATIONS IN RN

摘要

This paper is concerned with constructing radial solutions with arbitrarily many sign changes for quasilinear SchrOdinger equations in RN which have appeared as several models in mathematical physics. For any given integer k> 0, by using a minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem with double constraints, and by applying an energy comparison method we prove that the minimizer is indeed a solution of the quasilinear SchrOdinger equation.