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VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES
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作者 Ziyi ZHOU Yi JIANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1696-1706,共11页
For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle... For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas. 展开更多
关键词 maximal time function SUBDIFFERENTIAL normal cone nonsmooth analysis
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ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRDINGER EQUATION WITH A STARK POTENTIAL 被引量:1
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作者 朱世辉 张健 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1923-1938,共16页
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin... In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions. 展开更多
关键词 nonlinear Schrdinger equation blow-up solution blow-up point L2-concentration concentration compact principle
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LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL 被引量:1
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作者 朱世辉 张健 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1181-1192,共12页
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li... This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN |x|^2|u|^2dx 〈 +∞)}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that |u(t, x)|^2→ ||Q||L^2 2 δx=x1 as t → T. 展开更多
关键词 Nonlinear Schroedinger equation Stark potential blow-up solution limiting behavior mass concentration
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