摘要： In this talk, I will present our recent results about pseudo-parabolic equations and the Fucik spectrum for Kirchhoff type problem. Psudo-parabolic equations, as a class of reaction-diffusion equations, model the non-stationary analysis of the crystalline semiconductors. The Fucik spectrum is significant in many applications, for example, oscillations of suspension bridges. This lecture is first concerned with the global existence and blowup of solutions to a class of pseudo-parabolic equations. Particularly, I will present a sufficient and necessary condition under which the solution blows up in a finite time. Sequentially, some conclusions and applications on the Fucik spectrum for Kirchhoff type problem will be talked. The main result on this aspect is that we achieved three curves in the Fucik spectrum set of a class of Kirchhoff type problem with jumping nonlinearity. As an application, we obtain the multiplicity of solutions to a class of Kirchhoff type problems with the nonlinearity having extension property at both zero and infinity.
Our results presented were joint work with Zhanping Liang, Yuhua Li, Xiaoli Zhu and Ting Rong.
报告人简介：李福义, 教授, 博士生导师. 山西省教学名师, 山西省优秀科技工作者. 山西省数学会副理事长, 山西省工业与应用数学学会副理事长. 山西大学数学科学学院院长.