Infinitely Many Solutions for Sublinear Modified Nonlinear Schrodinger Equations Perturbed from Symmetry

In this paper, we consider the existence of infinitely many solutions for the following perturbed modified nonlinear 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 is an element of Omega, u = 0 x is an element of partial derivative Omega, where Omega is a bounded smooth domain in R-N (N >= 1) and alpha >= 2. Under the condition that g(x, u) is sublinear near origin with respect to u, we study the effect of non-odd perturbation term h(x, u) which breaks the symmetry of the associated energy functional. With the help of modified Rabinowitz's perturbation method and the truncation method, we prove that this equation possesses a sequence of small negative energy solutions approaching to zero.