报告题目(Title)：Multiplicity of positive and nodal solutions for scalar field equations

报告人(Speaker)：Prof. Giovanna Cerami (意大利Polytechnical University of Bari，教授）

时 间(Time)：2014年9月18日（星期四）16：00-17：00pm

地 点(Venue)：理科楼数学系A404

摘 要(Abstract)：The question of finding infinitely many changing sign solutions to the problem −？u+a(x)u = |u|^{p−1}u, in R^N, u∈H^1(R^N), is considered when N ≥ 2, p ≥ 1, p if N ≥ 3, and the potential a(x) is a positive function, which approaches its limit at infinity from above and which is not required to enjoy symmetry properties.

Assuming that a(x) satisfies a suitable “slow decay at infinity” condition and, more- over, that its graph has some “dips”, the existence of infinitely many nodal solutions will be shown by using a variational method.

报告人简介(Profile of speaker)：Giovanna Cerami是意大利女数学教授，是该国在变分与拓扑方法及其应用方面的专家之一。70年代提出现在所称的Cerami紧性条件；在没有紧性的非线性椭圆方程的研究方面取得重要成果。

联系人(Contact)：邹文明