Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Professor Kanishka Perera,Florida Institute of Technology, USA
Inviter:
Title:
A multiplicity result for the scalar field equation
Time & Venue:
2015.6.10 14:30-15:30 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.
Appendix：
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