1.報(bào)告題目：某些離散自治非線(xiàn)性薛定諤方程的基態(tài)解
摘要:In this talk, we will consider the existence of ground state solutions for a class of discrete nonlinear Schr?dinger equations with a sign-changing potential V that converges at infinity and a nonlinear term being asymptotically linear at infinity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is that, due to the convergency of V at infinity, the classical methods such as periodic translation technique and compact inclusion method cannot be employed directly to deal with the lack of compactness of the Cerami sequence. New techniques are developed in this work to overcome these two major difficulties. This enables us to establish the existence of a ground state solution and derive a necessary and sufficient condition for a special case. To the best of our knowledge, this is the first attempt in the literature on the existence of a ground state solution for the strongly indefinite problem under no periodicity condition on the bounded potential and the nonlinear term being asymptotically linear at infinity. This is a joint work with Genghong Lin and Jianshe Yu.
時(shí)間：2021年4月17日 周六上午 9:00-10：20
報(bào)告地點(diǎn)：北主樓1205微格教室
報(bào)告人簡(jiǎn)介：周展，廣州大學(xué)二級(jí)教授，博士生導(dǎo)師，教育部創(chuàng)新團(tuán)隊(duì)帶頭人，享受?chē)?guó)務(wù)院政府特殊津貼專(zhuān)家，廣州市“優(yōu)秀專(zhuān)家，先后主持創(chuàng)新團(tuán)隊(duì)發(fā)展計(jì)劃2項(xiàng)、國(guó)家自然科學(xué)基金6項(xiàng)，發(fā)表學(xué)術(shù)論文80余篇。
2.報(bào)告題目：時(shí)間離散的時(shí)滯反應(yīng)擴(kuò)散方程的波前解
摘要:With the growth of a single species with age structure on an unbounded domain as a prototype, we derive a delayed temporally discrete reaction-diffusion equation. The main result is on the existence of traveling wavefront solutions of the equation. We first transform the problem into that on the existence of fixed points of a mapping. Then by successfully constructing a pair of upper and lower solutions, we establish the existence of traveling wavefront by applying the upper-lower solution method.
時(shí)間：2021年4月17日 周六上午 10:30-11：50
報(bào)告地點(diǎn)：北主樓1205微格教室
報(bào)告人簡(jiǎn)介：郭志明，廣州大學(xué)教授，博士生導(dǎo)師，南粵優(yōu)秀教師，廣州市優(yōu)秀教師，先后主持國(guó)家自然科學(xué)基金面上項(xiàng)目3項(xiàng)，參加國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目1項(xiàng)，發(fā)表學(xué)術(shù)論文70余篇。
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五邑大學(xué)學(xué)科與科技（社科）發(fā)展中心
數(shù)學(xué)與計(jì)算科學(xué)學(xué)院
2021年4月14日
