DYNAMICS OF RADIAL THRESHOLD SOLUTIONS FOR GENERALIZED ENERGY-CRITICAL HARTREE EQUATION

作     者：Li, Xuemei Liu, Chenxi Tang, Xingdong Xu, Guixiang 

作者机构：Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China School of Mathematics and Statistics Nanjing Univeristy of Information Science and Technology Nanjing210044 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Ground state 

摘      要：In this paper, we study long time dynamics of radial threshold solutions for the focusing, generalized energy-critical Hartree equation and classify all radial threshold solutions. The main arguments are the spectral theory of the linearized operator, the modulational analysis and the concentration compactness rigidity argument developed by T. Duyckaerts and F. Merle to classify all threshold solutions for the energy critical NLS and NLW in [18, 19], later by D. Li and X. Zhang in [43, 44] in higher dimensions. The new ingredient here is to solve the nondegeneracy of positive bubble solutions with nonlocal structure in H1(RN) (i.e. the spectral assumption in [51]) by the nondegeneracy result of positive bubble solution in L∞(RN) in [45] and the Moser iteration method in [16], which is related to the spectral analysis of the linearized operator with nonlocal structure, and plays a key role in the construction of the special threshold solutions, and the classification of all threshold solutions. © 2023, CC BY.