On Lane-Emden type equations on the integer lattice graphs

Speaker: 周风 (华东师范大学)

Time: 2026-01-30 13:30-17:30
Location: 1110, SIMIS

摘要：

We will talk about the existence and nonexistence of positive solutions to Lane- Emden type equations with a potential on the d-dimensional integer lattice graph $Z^d$, as well as in the half-space and quadrant domains, under the zero Dirichlet boundary condition in the latter two cases. The existence result is established via variational methods, while in contrast, the nonexistence is obtained  by iteratively analyzing the decay behavior at infinity. This is based on joint work with HY Chen and BB Hua.

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About Speaker:

周风教授，1980年本科就读武汉大学数学系。1985年公派留学法国,1993年获得巴黎第六大学数学博士学位。 曾入选为上海市曙光学者，上海市优秀学科带头人。曾主持教育部和国家外专局的“数学创新引智”计划。其研究领域为非线性偏微分方程。主要感兴趣于研究几何、数学物理中非线性偏微分方程解的性态及相关问题。研究成果发表在CPAM，Ann. Inst. H. Poincare–AN，JFA， Calc. Var. PDEs, JDE, Science China等数学期刊上。