报告题目：On normalized solutions of (2, q)–Laplacian equations in

报 告 人：Patrizia Pucci

报告时间：9.26（星期五）16:00-16:45

报告地点：数统大楼学术报告厅103

摘要： Motivated by a wide range of applications in physics and related sciences, such as plasma physics, biophysics, and chemical reaction design,  in this talk we first present existence and multiplicity of normalized solutions to the following (2,q)-Laplacian equation

where  is the  q-Laplacian of , with

,

is an unknown parameter that appears as a Lagrange multiplier, c > 0 is a constant and  

The nonlinearity  is continuous and the behaviour of g at the origin is allowed to be strongly sublinear, i.e., , which includes the logarithmic nonlinearity

We consider a family of approximating problems that can be set in X and the corresponding least-energy solutions. Then, we prove that such a family of solutions converges to a least-energy solution to the original problem (). Additionally, under certain assumptions on g that allow us to work in a suitable subspace of X,  we prove the existence of infinitely many solutions of the (2,q)-Laplacian equation().

Joint work with R. Ding and C. Ji from Shangha

报告人简介：

意大利著名女数学家Patrizia Pucci院士，主要从事非线性分析与偏微分方程研究，尤其在非线性椭圆型方程和分数阶算子领域有深厚造诣。 ‌她于佩鲁贾大学完成博士学业，已在 Acta of Math 等许多重要数学刊物发表了二百多篇学术论文，出版专著3部，包括经典著作《The Maximum Principle》。其研究成果在在WoS（Web of Science）引用数据库中，总共有199篇论文被引用7358次，h指数为42。 2016年获罗马尼亚克拉约瓦大学荣誉博士学位。2017年获Babes Bolyai大学的荣誉博士学位，并成为翁布里亚科学院成员。2018-2021年获由Clarivate Analytics 颁发的高被引作者。2019年成为Peloritana Pericolanti 自然科学研究院数学物理类研究员。