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Yanheng Ding--Some results on strongly indefinite variational problems (1)
发布人:管理员LIU  发布时间:2017-07-16   浏览次数:498


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.


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