In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a sm...In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, I<sub>α</sub> is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .展开更多
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the conditio...The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.展开更多
In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on t...In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.展开更多
This short note is concerned with a measure version criterion for hypersurfaces to be minimal.Certain natural flows and associated reflections for many minimal hypercones,including minimal isoparametric hypercones and...This short note is concerned with a measure version criterion for hypersurfaces to be minimal.Certain natural flows and associated reflections for many minimal hypercones,including minimal isoparametric hypercones and area-minimizing hypercones,are studied.展开更多
文摘In this paper, we study the following quasilinear equation of choquard type: where A(x,t) is given real functions on R<sup>N</sup> × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, I<sub>α</sub> is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique. .
文摘The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11631007 and 11971251).
文摘In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.
基金Supported by NSFC (Grant Nos. 11971352, 11601071)the S. S. Chern Foundation through IHES and a Start-up Research Fund from Tongji University。
文摘This short note is concerned with a measure version criterion for hypersurfaces to be minimal.Certain natural flows and associated reflections for many minimal hypercones,including minimal isoparametric hypercones and area-minimizing hypercones,are studied.
