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金伏生. 非线性问题严格互补极点-鞍点定理[J]. 力学学报, 1994, 26(2): 214-221. DOI: 10.6052/0459-1879-1994-2-1995-539
引用本文: 金伏生. 非线性问题严格互补极点-鞍点定理[J]. 力学学报, 1994, 26(2): 214-221. DOI: 10.6052/0459-1879-1994-2-1995-539
THE STRICT COMPLEMENTARY EXTREMUM-SADDLE POINT THEOREM IN NONLINEAR PROBLEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 214-221. DOI: 10.6052/0459-1879-1994-2-1995-539
Citation: THE STRICT COMPLEMENTARY EXTREMUM-SADDLE POINT THEOREM IN NONLINEAR PROBLEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 214-221. DOI: 10.6052/0459-1879-1994-2-1995-539

非线性问题严格互补极点-鞍点定理

THE STRICT COMPLEMENTARY EXTREMUM-SADDLE POINT THEOREM IN NONLINEAR PROBLEMS

  • 摘要: 本文给出两个具有新的非线性型式问题的严格互补极点-鞍点定理,同时论述了建议的二次变分-凸分析方法的一般性和有效性。其一是旋转叶轮问题,通过引进周期性自由面变量,揭示了隐含的一类对偶变分原理,从而给出了可能存在的全部互补原理。其二是带转动变量的非K-L壳体,具有超出常规的几何非线性性质,目前只知道使用这里的方法可以建立互补原理。

     

    Abstract: The strict complementary extremum-saddle point theorem for two prob-lems of new nonlinear form are obtained,and the generality and effectiveness for secondvariation-convex analysis method suggested are demonstrated in this paper.The first prob-lem is rotating tubro impeller,and by introducing the periodic free surface variable we obtainall complementary variational principles.The second problem is non K-L shell with rotaryvaridfble having specific nonlinear geometrical property,and we establish the comple...

     

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