Academic report on“Existence of solutions for Schrödinger systems with linear and nonlinear couplings”

Academic report on“Existence of solutions for Schrödinger systems with linear and nonlinear couplings”

At the invitation of Center for Mathematical Sciences and School of Mathematics and Physics of CUG, Professor Zhitao Zhang from Chinese Academy of Sciences gave an online talk titled “Existence of solutions for Schrödinger systems with linear and nonlinear couplings” on Nov 19th, 2020. Teachers and students in School of Mathematics and Physics in related research fields attended this academic colloquium. Teachers and students from relevant research fields of the School of Mathematical Physics attended the symposium.

Prof. Zhang has long been engaged in nonlinear functional analysis theory and has published 1 academic monograph in Springer and nearly 90 papers in such prestigious journals as Journal of Functional Analysis, Annales de l'Institut Henri Poincare Analyse Non Lineaire, J. Differential Equations, Calculus of Variations and PDE, Transactions of the American Mathematical Society, etc. In the difficult free boundary problem, Bose-Einstein condensatesSchrodinger equations, biological competition equations and many other aspects, Prof. Zhang has made important results, and solved the difficult Terracini conjecture and the 3-dimensional Henon-Lane-Emden conjecture.

In this talk, Prof. Zhang mainly introduced the existence of ground state and bound state solutions for Schrödinger systems with linear and nonlinear couplings arising from Bose Einstein Condensates, the bifurcation, symmetric results, and asymptotic properties of the solutions are included.The symposium was rich in content and novel in scientific research methods. The teachers and students were deeply inspired.After the colloquium, Prof. Zhang had a detailed exchange and discussion with teachers and students. The colloquium ended smoothly in a warm atmosphere.