数学科学系

Department of Mathematical Sciences

Multiplicity of positive and nodal solutions for scalar field equations

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)

 

  (Time)2014918日(星期四)1600-1700pm

 

  (Venue):理科楼数学系A404

 

  (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 < 2N/(N − 2))  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