By Chungen Liu

Within the final 40 years, nonlinear research has been largely and speedily built. Lectures provided within the overseas convention on Variational equipment on the Chern Institute of arithmetic in Tianjin of may possibly 2009 mirror this improvement from assorted angles. This quantity includes articles in response to lectures within the following parts of nonlinear research: severe element idea, Hamiltonian dynamics, partial differential equations and platforms, KAM thought, bifurcation thought, symplectic geometry, geometrical research, and celestial mechanics. combos of topological, analytical (especially variational), geometrical, and algebraic equipment in those researches play very important roles. during this court cases, introductory fabrics on new theories and surveys on conventional themes also are given. extra views and open difficulties on hopeful examine subject matters in comparable parts are defined and proposed. Researchers, graduate and postgraduate scholars from a variety of parts in arithmetic and physics will locate contents during this lawsuits are worthwhile.

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40. M. Vega, Travelling wavefronts of reaction-diffusion equations in cylindrical domains, Comm. PDE 18 (1993), 505-530. 41. M. Vega, The asymptotic behavior of the solutions of some semilinear elliptic equations in cylindrical domains, J. Differential Equations 102 (1993), August 3, 2010 13:56 WSPC - Proceedings Trim Size: 9in x 6in variational Turing patterns and standing waves 39 119-152. 42. M. Vega, On the uniqueness of multidimensional travelling fronts of some semilinear equations, J. Math.

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Unfortunately, they also depend on the numerical results. QUESTION 3. Give a mathematical proof of this symplectic Jordan form. 4 We should point out that the stability of the figure-eight is quite special among the solutions found recently by minimization methods. In fact numerical simulations show that it is one of several examples of stable solutions, and the others are all unstable. Our theorem on the instability of periodic orbit, degenerate or not, via Maslov index will be useful for this purpose.

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