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关于一类无下界函数的变分问题的一个注记 被引量：4

A Note on Variational Principle of Functions which are Unbounded Below
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摘要 本文给出了在每个有界子集上有下界的下半连续广义实值函数的一个光滑变分原理. This paper gives a smooth variational principle of lower semicontinuous functions which are bounded below on each bounded set.
作者 骆道忠
机构地区 厦门大学数学科学学院
出处 《数学研究》 CSCD 2005年第4期383-385,共3页 Journal of Mathematical Study
基金 国家自然科学基金资助项目(10471114)
关键词 下半连续函数 β-可微性 变分原理 BANACH空间 lower semicontinuous function β-differentiability variational principle Banach space
分类号 O176 [理学—基础数学]
  • 相关文献

参考文献4

  • 1Phelps R R.Convex functions,monotone operators and differentiability.Lect.Notes in Math.Springer-verlag,1989.
  • 2Borwein J,Preiss D.A smooth variational principle with applications to subdifferentiability,and to differentiability of convex functions,Trans.Amer.Math Soc,1987,303:517-527.
  • 3Ekeland I.On the variational principle,J.Math.Anal Appl,1974,47:324-353.
  • 4Deville R,Godefroy G.and Zizler V.E.A smooth variational principle with applications to Hamilton-Jacobi equations in infinite dimensions,J.Funct.Anal,1993,111:192-212.

同被引文献12

  • 1Bosch C, Garcia A and Garcia C L. An extension of Ekeland ' variational principle to locally complete spaces [ J ]. Mathematical Analysis and Applications, 2007,328 : 106 - 108.
  • 2Qiu Jinghui . The density of extremal points in Ekeland' variational principle [ J ]. Mathematical Analysis and Applications, 2007,328 : 946 - 957.
  • 3Marian Fabian and Catherine Finet. On Stegall' s smooth variational principle [ J]. Nonlinear Analysis ,2007,66 : 565 - 570.
  • 4Phelps R R. Convex functions, monotone operators and differentiability. Lecture Notes in Mathematics [ M ]. Berlin : Springer-Verlag, 1993 : 1364.
  • 5Ekeland I. On. the Variational Principle[ J]. Math Appl, 1974, (47) :324 -353.
  • 6Borwein J, Preiss D. A Smooth Variational Principle with Applications to Subdifferentiability and to Differentiability of Convex Functions [ J ]. Trans Amer Math Soc, 1987,303 : 517 - 527.
  • 7Deville R, Godefroy G, Zizler V E. A Smooth Variational Principle with Applications to Hamilton-Jacobi Equations in Infinite Dimensions [ J ]. Funct Anal, 1993,111 : 197 - 212.
  • 8Qiu Jinghui. The Density of Extremal Points in Ekeland' Variational Principle [ J ]. Math Anal Appl,2007 ,328 :946 -957.
  • 9Marian Fabian, Catherine Finet. On Stegall' s Smooth Variational Principle [ J ]. Nonlinear Analysis,2007,66:565 - 570.
  • 10Phelps R R. Convex Functions, Monotone Operators and Differentiability [ M ]//Lecture Notes in Mathematics. Berlin / New York : Springer-Verlag, 1993.

引证文献4

数学研究
2005年 第4期

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