广州数学大讲坛第七期
第六十二讲——中央民族大学郭青教授学术报告
题目：Existence and Non-degeneracy of Peak Solutions for Logarithmic Scalar Field Equations
时间: 2024年10月9日(星期三)晚上 19:00-21:30
地点: 腾讯会议（会议ID：914-185-996）
报告人：郭青 教授
摘要： We are concerned with a class of important Schrödinger equations in mathematical physics with logarithmic nonlinearities, establishing the existence of positive peak solutions. The primary challenges in applying the Lyapunov-Schmidt reduction to logarithmic scalar equations arise from the non-smooth nature and sublinear growth of the logarithmic nonlinearity. Our approach is based on a novel inner-outer decomposition, distinguishing it from the traditional gluing techniques. Furthermore, by employing the local Pohozaev identity technique, we obtain non-degeneracy results for the multi-peak solutions.
