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A multiplicity result for the scalar field equation
【2015.6.10 2:30pm, N818】

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 2015-5-28 

  Colloquia & Seminars 

  Speaker

Professor Kanishka Perera,Florida Institute of Technology, USA

  Title

A multiplicity result for the scalar field equation 

  Time

2015.6.10 14:30-15:30

  Venue

N818

  Abstract

We prove the existence of $N – 1$ distinct pairs of nontrivial solutions of the scalar field equation in $\R^N$ under a slow decay condition on the potential near infinity, without any symmetry assumptions. Our result gives more solutions than the existing results in the literature when $N \ge 6$. When the ground state is the only positive solution, we also obtain the stronger result that at least $N – 1$ of the first $N$ minimax levels are critical, i.e., we locate our solutions on particular energy levels with variational characterizations. Finally we prove a symmetry breaking result when the potential is radial. To overcome the difficulties arising from the lack of compactness we use the concentration compactness principle of Lions, expressed as a suitable profile decomposition for critical sequences.   

  Affiliation

 

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