Sign-changing solutions for modified nonlinear Schröinger equation

In this paper, we consider the following modified nonlinear Schrodinger equation: ???1319-01??? This type of equations have been involved in models of mathematical physics, and mathematical work has been done extensively in recent years. The problem has a formal variational structure, but it is difficult to find a suitable space in which the variational functional possesses both smoothness and compactness properties. We introduce a p-Laplacian perturbation approach, obtain solutions of the perturbed problems as approximate solutions of the original problem, and establish suitable estimates for these solutions. Then we pass limits to get solutions of the original problem. We prove the existence of infinitely many sign-changing solutions with the integral constraint ∫ R N | u | p dx = 1, where λ appears as a Lagrangian multiplier.