非线性分析研讨班：Existence and symmetry of positive solutions to nonlocal Schrödinger-Poisson systems in the fractional Sobolev limiting case

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：刘志苏教授   中国地质大学（武汉）

题  目：Existence and symmetry of positive solutions to nonlocal Schrödinger-Poisson systems in the fractional Sobolev limiting case

时  间：2024.08.04（星期日）10：00-11：00

地  点：N818

摘  要：In this report, we consider the existence of positive solutions for nonlocal systems in gradient form and set in the whole R^N. That is, a quasilinear fractional Schrödinger equation, where the leading operator is the fractional Laplacian, is coupled with a higher-order and possibly fractional Poisson equation. For both operators the dimension N≥ 2 corresponds to the limiting case of the Sobolev embedding, hence we consider nonlinearities with exponential growth. Since standard variational tools cannot be applied due to the sign changing logarithmic Riesz kernel of the Poisson equation, we employ a variational approximating procedure for an auxiliary Choquard equation, where the Riesz kernel is uniformly approximated by polynomial kernels. Qualitative properties of solutions such as symmetry, regularity and decay are also established.