PDE Seminar Abstracts

Uniqueness, existence and concentration of positive ground states for Kirchhoff type problems

Zhitao Zhang
Chinese Academy of Sciences, China
Wed 16th Nov 2016, 3-4pm, Carslaw Lecture Theater 375


Kirchhoff type equations have been studied extensively by many researchers, which is related to the stationary analogue of the equation proposed by Kirchhoff as an extension of the classical D’Alembert wave equation for free vibrations of elastic strings, Kirchhoff’s model takes into account the changes in length of the string produced by transverse vibrations.

We first show some recent results on nonlocal problems. We prove the uniqueness of positive ground state for the Kirchhoff type equations with constant coefficients Then we use the uniqueness results to obtain the existence and concentration theorems of positive ground states to the Kirchhoff type equations with competing potential functions for a sufficiently small positive parameter ϵ.