Topic:Existence and Uniqueness of solutions for some Kirchhoff equations
Speaker: Professor ZhangYimin
Event date: 4/26/2019
Event time: 10:00
Venue: Lecture Hall 204,Building 9
Sponsor: School ofMathematics and Statics, Institute of Science and Technology
Abstract: For some Kirchhofffunctionals, we search for its $L^2$-normalized critical points. Firstly, we givea complete classification with respect to the exponent $p$ for the existence ofminimizers of these functionals, and show that the minimizer of thesefunctionals, if exists, is unique up to translations. Secondly, we search forthe mountain pass type critical point for these functionals on $L^2$ constraintmanifold, and also prove that this type critical point is unique up totranslations. Our proof relies only on some simple energy estimates and avoidsusing the concentration-compactness principles.These conclusions extend someknown results in previous papers.