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【和山數學論壇185期】浙江師范大學沈自飛教授學術報告

來源:浙江科技學院理學院 | 2019-05-27 | 發布:經管之家



一、題目:On critical Choquard equation with potential wel



二、主講人:沈自飛教授、博士生導師



三、時間:5月30日(周四)下午13:30-14:30
四、地點:A4-305報告廳



摘要:In this paper we are interested in the following nonlinear Choquard equation$$-\Deltau+(\lambdaV(x)-\beta)u=\big(|x|^{-\mu}\ast|u|^{2_{\mu}^{\ast}}\big)|u|^{2_{\mu}^{\ast}-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N,$$where $\lambda,\beta\in\mathbb{R}^+$,$0<\mu<N$, $N\geq4$, $2_{\mu}^{\ast}=(2N-\mu)/(N-2)$ is the upper critical exponent due to the Hardy-Littlewood-Sobolev inequality and the nonnegativepotential function $V\in \mathcal{C}(\mathbb{R}^N,\mathbb{R})$ such that $\Omega :=\mbox{int} V^{-1}(0)$ is a nonempty bounded set with smooth boundary. If $\beta>0$ is a constant such that the operator $-\Delta +\lambda V(x)-\beta$ is non-degenerate, we prove the existence of ground state solutions which localize near the potential well int$V^{-1}(0)$ for $\lambda$ large enough and also characterize the asymptotic behavior of the solutions as the parameter $\lambda$ goes to infinity. Furthermore, for any $0<\beta<\beta_{1}$, we are able to prove the existence of multiple solutions by the Lusternik-Schnirelmann category theory, where $\beta_{1}$ is the first eigenvalue of $-\Delta$ on $\Omega$ with Dirichlet boundary condition.






報告人簡介:沈自飛,浙江諸暨人,中共黨員,教授、博導。曾任浙江師范大學數學系副主任,數理學院副院長。現為浙江師范大學學術期刊社副社長、學報(自然科學版)副主編、《中學教研》雜志主編,核心期刊《數學教育學報》董事會副董長。浙江省高校中青年學科帶頭人,省重點建設專業“數學與應用數學”專業負責人,基礎數學碩士點負責人。







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