# 太阳网集团8722

 Seminars and Talks
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 Yanheng Ding--Some results on strongly indefinite variational problems (2)
 发布人：管理员LIU  发布时间：2017-07-17   浏览次数:496
 Abstract: Consider the following general nonlinear system   Au = N(u)                 (1)where H is a Hilbert space, A is a self-adjoint operator, and N is a (nonlinear) gradient operator. Typical example are Dirac equations and reaction-diffusion systems where \sigma(A) (the spectrum) is unbounded from below and above, and particularly, \sigma_e(A)\cap\mathbb R^{\pm}\not=\empty. The talk focus on     1)  to establish general variational setting for (1) by using the operator interpolation theory;     2) certain critical point theory;     3) the existence, concentration and exponential decay for semi-classical solutions of Dirac equation and the reaction-diffusion systems, etc.;     4) bifurcation of Dirac equation on spin manifolds.