Abstract: Inspired by the work in Zhou and Li (SISC , 2001,2002) and the line search rules in optimization theory in R^n aiming at the global convergence, in this talk we propose a modified Local Minimax Method(LMM) based on a normalized Goldstein line search rule to find multiple minimax-type solutions. The feasibility of our approach is provided and its corresponding convergence is proven. Finally, our approach is implemented to solve several typical semilinear elliptic boundary value problems on a square for multiple saddle points and the numerical results indicate that our approach is efficient.
