第二次变异的功能决定因素

IF 1.4 3区数学 Q1 MATHEMATICS

Journal of Fixed Point Theory and Applications Pub Date : 2024-03-23 DOI:10.1007/s11784-024-01100-3

Stefano Baranzini

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引用次数: 0

摘要

我们研究了一般边界条件下最优控制问题的二次变式的行列式。一般来说，这些算子不是迹类，行列式被定义为主值极限。我们提供了一个公式，用外差流的线性化来计算这个行列式。我们在一些特殊情况下说明了这一过程，并证明了一些希尔式公式。

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Functional determinants for the second variation

We study the determinant of the second variation of an optimal control problem for general boundary conditions. Generically, these operators are not trace class and the determinant is defined as a principal value limit. We provide a formula to compute this determinant in terms of the linearisation of the extrenal flow. We illustrate the procedure in some special cases, proving some Hill-type formulas.

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来源期刊

Journal of Fixed Point Theory and Applications 数学-数学

CiteScore

3.10

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Fixed Point Theory and Applications (JFPTA) provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Research topics include but are not limited to: (i) New developments in fixed point theory as well as in related topological methods, in particular: Degree and fixed point index for various types of maps, Algebraic topology methods in the context of the Leray-Schauder theory, Lefschetz and Nielsen theories, Borsuk-Ulam type results, Vietoris fractions and fixed points for set-valued maps. (ii) Ramifications to global analysis, dynamical systems and symplectic topology, in particular: Degree and Conley Index in the study of non-linear phenomena, Lusternik-Schnirelmann and Morse theoretic methods, Floer Homology and Hamiltonian Systems, Elliptic complexes and the Atiyah-Bott fixed point theorem, Symplectic fixed point theorems and results related to the Arnold Conjecture. (iii) Significant applications in nonlinear analysis, mathematical economics and computation theory, in particular: Bifurcation theory and non-linear PDE-s, Convex analysis and variational inequalities, KKM-maps, theory of games and economics, Fixed point algorithms for computing fixed points. (iv) Contributions to important problems in geometry, fluid dynamics and mathematical physics, in particular: Global Riemannian geometry, Nonlinear problems in fluid mechanics.