報(bào)告人：郭宗明 教授

報(bào)告題目：Slow-decay solutions for some elliptic equations in exterior domains

報(bào)告時(shí)間：2025年10月11日（周六）上午8：00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

郭宗明，河南師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院教授，理學(xué)博士、博士生導(dǎo)師、河南省特聘教授。曾任中國(guó)數(shù)學(xué)會(huì)理事、河南省數(shù)學(xué)會(huì)理事長(zhǎng)、河南師范大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院院長(zhǎng)、河南師范大學(xué)校學(xué)術(shù)委員會(huì)副主任。長(zhǎng)期從事非線(xiàn)性偏微分方程與泛函分析領(lǐng)域的教學(xué)科研工作。他于1982年獲新鄉(xiāng)師范學(xué)院（現(xiàn)河南師范大學(xué)）數(shù)學(xué)學(xué)士學(xué)位，1987年在中國(guó)科學(xué)院數(shù)學(xué)所獲碩士學(xué)位，1992年獲英國(guó)格拉斯哥大學(xué)數(shù)學(xué)博士學(xué)位，并在澳大利亞新英格蘭大學(xué)和悉尼大學(xué)完成博士后研究。

報(bào)告摘要：

We are interested in structure of positive solutions for some elliptic problems in exterior domains.It is well-known that Liouville-type results can be obtained for subcritical and critical cases of the problems. This means that the problems with subcritical and critical exponents do not admit nontrivial nonnegative solutions in exterior domains. In supercritical case, the problems admit positive radial fast-decay solutions. But the exact structure of positive fast-decay and slow-decay solutions for the problems is still unclear. We construct infinitely many positive slow-decay solutions for the problems via asymptotic expansions of prescribed solutions of the problems at an isolated singular point and sub- and super-solution argument.