Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 缑天祥 博士，西安交通大学
| | Inviter: | | Title:
| Higher topological type semiclassical states for fractional nonlinear elliptic equations | Time & Venue:
| 2021.12.07 16：00-17:00 腾讯会议：281 782 379 | Abstract:
| In this talk, we are concerned with semiclassical states to fractional nonlinear elliptic equations in the Sobolev subcritical, critical and supercritical cases. We construct positive semiclassical states and an infinite sequence of sign-changing semiclassical states with higher energies clustering near the local minimum points of the potential. The solutions are of higher topological type, which are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. They correspond to critical points of the underlying energy functional at energy levels where compactness condition breaks down. The proofs are mainly based on penalization methods, s-harmonic extension theories and blow-up arguments along with local type Pohozaev identities. This is a joint work with. Prof. Shaowei Chen.
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