Colloquium| Institute of Mathematical Sciences
Time：10:30-11:30, December 5 Thursday
Location：Room S408, IMS
Speaker: Professor Quoc-Anh Ngo from VietNam National University
Abstract: This talk concerns classical, non-trivial, non-negative solutions to the simplest models of polyharmonic equations with power-type nonlinearity
\[
Δ^m u = ± u^α
\]
in R^n with n ≥ 1, m ≥1, and α is real. For small m, the above equations arise in many physical phenomena and applied mathematics. They also arise from several prescribing geometric curvature problems in conformal geometry such as the Yamabe problem, the scalar curvature problem, and the Q-curvature problem for the Paneitz operator. Higher-order cases also arise from the Q-curvature problem, however, for the GJMS operators. In this talk, I will present a complete picture of the existence and non-existence of solutions to the above equations in the full rage of the parameters n, m, and α. I also discuss a complete picture of the positivity of solutions to the above equations. This is joint work with V.H. Nguyen, Q.H. Phan, and D. Ye.