In the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.

On 2-Tori Having a Pole (V Bangert); Turing Patterns and Standing Waves in Fitzhugh-Nagumo Type Systems (C-N Chen & S-Y Kung); Remarks on Mean Value Properties (Y Y Li & L Nguyen); Brake Orbits in Bounded Convex Symmetric Domains (C Liu & D Zhang); Recent Progress on Closed Geodesics in Some Compact Simply Connected Manifolds (Y Long); Topological Bifurcation Theory: Old and New (J Mawhin); Exponential Growth Rate of Paths and Its Connection with Dynamics (Z Xia & P Zhang); Rabinowitz's Theorems Revisited (W Zou); and other papers.