Infinitely many solutions for indefinite quasilinear Schrodinger equations under broken symmetry situations

In this paper, we study the existence of infinitely many solutions for the indefinite quasilinear Schrodinger equations {-Delta u - Delta(vertical bar u vertical bar(alpha))vertical bar u vertical bar(alpha-2)u = g(x,u) + h(x,u), x epsilon Omega, u = 0, x epsilon partial derivative Omega, where alpha >= 2, g, h epsilon C((Omega) over bar x R, R). When g(x, u) is only of locally superlinear growth at infinity in u and h(x, u) is not odd in u, the existence of infinitely many solutions is proved in spite of the lack of the symmetry of this problem by using dual approach and Bolle's perturbation method. Our results generalize some known results and are new even in the symmetric situation. Copyright (C) 2016 John Wiley & Sons, Ltd.