报告题目:Segregated solutions for nonlinear Schrödinger systems with sublinear coupling terms

报告人:张程翔副教授（北京师范大学）

报告时间:2026年03月28日09：30-11：30

报告地点:数学与统计学院145会议室

报告摘要:In this paper, we establish the existence of infinitely many nonnegative, segregated solutions for nonlinear Schrödinger systems with sublinear coupling terms. The sublinear coupling exponents introduce fundamental challenges due to nonsmooth nonlinearities and singularities in the linearized operator, which render standard reduction methods inapplicable. To overcome these obstacles, we develop an enhanced Lyapunov-Schmidt reduction framework. By recasting the reduction process as a fixed point problem within a specially constructed metric space formed by local minimizers of an associated outer boundary value problem, we derive sharp a priori decay estimates that enable rigorous contraction mapping arguments. This approach successfully circumvents the limitations of classical methods regarding sublinear couplings. Furthermore, we uncover a novel"dead core"phenomenon in this regime: the constructed solutions exhibit non-strict positivity, with component supports separating in specific regions, particularly characterized by annular segregation in two-dimensional spaces. This is a joint work with Prof. Qing Guo.

报告人简介:张程翔，北京师范大学副教授，主要研究方向为偏微分方程与非线性泛函分析，在非线性薛定谔方程的解结构方面取得了突出成果。其研究聚焦于正规化多包解，探讨该类解在量子力学、光学等物理领域中的应用；同时，系统研究对数型薛定谔方程的束缚态，解决势函数在奇异点及无穷远处解的存在性等关键问题。在Arch.Ration.Mech.An.，Cal. Var. PDE，INDIANA.U.MATH.J.，J. Math. Pures Appl.，Nonlinearity等权威学术期刊上发表多篇学术论文，主持多项国家自然科学基金。