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學(xué)術(shù)報(bào)告  (2019020)

報(bào)告題目 ：Local linking anbd indefinite Schrodinger equations

報(bào)告人：劉軾波教授（廈門大學(xué)）

報(bào)告地點(diǎn)：理學(xué)實(shí)驗(yàn)樓312報(bào)告廳

報(bào)告時(shí)間：2019年4月30日下午 2：30-3：30

Abstract ：The study of stationary Schrodinger equations has a long history. Even for the case that the Schrodinger operator is indefinite, many interesting results has been obtained by linking theorems.

In recent years, more general Schrodinger type equations such as Schrodinger-Poisson systems, quasilinear Schrodinger equations, have captured great interest. Most study focus on the case that the Schrodinger operator is definite so that the zero function is a local minimizer of the energy functional. We discovered that for such equations, unlike the classical Schrodinger equations mentioned above, when the Schrodinger operator is indefinite, the linking theorems is not applicable.

Fortunately, we found that the local linking theory of Shujie Li and Jiaquan Liu is quite suitable for treating this kind of problems. In this talk, we will demostrate how local linking could be applied to indefinite Schrodinger-Poisson systems, quasilinear Schrodinger equations, and fourth order elliptic equations with the Laplacian of u^2.

報(bào)告人簡介：劉軾波, 男, 1975年生于廣東. 在蘭州大學(xué)獲得學(xué)士和碩士學(xué)位后, 到中國科學(xué)院數(shù)學(xué)所學(xué)習(xí), 于2003年獲得博士學(xué)位. 2005年從北京大學(xué)數(shù)學(xué)研究所博士后出站, 到廈門大學(xué)任副教授. 2008年任汕頭大學(xué)教授, 2011年任廈門大學(xué)教授. 現(xiàn)為廈門大學(xué)數(shù)學(xué)系教授、博士生導(dǎo)師. 先后主持國家自然科學(xué)基金青年項(xiàng)目和面上項(xiàng)目, 以及福建省杰出青年基金項(xiàng)目. 2013年入選意大利國際理論物理中心(ICTP)協(xié)聯(lián)成員, 2017年受國家留學(xué)基金委資助到美國圣母大學(xué)訪問一年. 他的研究領(lǐng)域是非線性泛函分析、非線性偏微分方程的變分方法.

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