共查询到20条相似文献,搜索用时 0 毫秒
1.
S. Kumagai 《Journal of Optimization Theory and Applications》1980,31(2):285-288
In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:R
n ×R
m R
n, withF(x
0,y
0)=0, that requires neither differentiability ofF nor nonsingularity of
x
F(x
0,y
0). In the proof, the local one-to-one condition forF(·,y):A R
n R
n for ally B is consciously or unconsciously treated as implying thatF(·,y) mapsA one-to-one ontoF(A, y) for ally B, and the proof is not perfect. A proof can be given directly, and the theorem is shown to be the strongest, in the sense that the condition is truly if and only if. 相似文献
2.
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved
being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie subgroup
problem for Banach–Lie groups, as well as Weil’s local rigidity for homomorphisms from finitely generated groups to Banach–Lie
groups.
相似文献
3.
Andreas Johann 《Journal of Mathematical Analysis and Applications》2010,367(2):389-400
We deal with the continuum limit of lattice differential equations and show how an implicit function theorem of Craven and Nashed can be used in order to continuate solutions of the resulting partial differential equation to solutions of the original spatially discrete system. 相似文献
4.
Martin Väth 《Annali di Matematica Pura ed Applicata》2007,186(2):199-227
We show some abstract (purely set-topological) principles which allow to prove the existence of global solution branches.
The results apply either for the locally compact situation and then allow to prove global bifurcation results of Rabinowitz
type, or they apply for a locally connected situation and allow to prove global branches of arbitrarily small perturbations
without any compactness hypotheses. As two applications, we obtain a generalization of the Rabinowitz theorem for bifurcation
from an interval and an implicit function type theorem for nondifferentiable functions. 相似文献
5.
I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue's dominated convergence theorem and Ekeland's variational principle. As a consequence, the assumptions are substantially weakened: the map F to be inverted is not required to be C2, or even C1, or even Fréchet-differentiable. 相似文献
6.
Generalized implicit function theorem and its application to parametric optimal control problems 总被引:1,自引:0,他引:1
Ekaterina Kostina Olga Kostyukova 《Journal of Mathematical Analysis and Applications》2006,320(2):736-755
Many problems in physics and mathematics may be reduced to solving equations depending on a parameter. The justification of the existence of solutions to the equations and the sensitivity analysis may be conducted based on Implicit Function Theorem (IFT) under certain regularity assumptions. Provided the regularity assumptions do not hold, generalizations of IFT are needed in order to study solutions to the equations. The paper focuses on a particular generalization of IFT which is then applied to a parametric linear time-optimal control problem. 相似文献
7.
The aim of this paper is to develop the Floquet theory for linear implicit difference systems (LIDS). It is proved that any index-1 LIDS can be transformed into its Kronecker normal form. Then the Floquet theorem on the representation of the fundamental matrix of index-1 periodic LIDS has been established. As an immediate consequence, the Lyapunov reduction theorem is proved. Some applications of the obtained results are discussed. 相似文献
8.
The implicit function theorem (IFT) can be used to deduce the differentiability of an implicit mapping S:u?y given by the equation e(y,u)=0. However, the IFT is not applicable when different norms are necessary for the differentiation of e w.r.t. y and the invertibility of the partial derivative ey(y,u). We prove theorems ensuring the (twice) differentiability of the mapping S which can be applied in this case. We highlight the application of our results to quasilinear partial differential equations whose principal part depends nonlinearly on the gradient of the state ∇y. 相似文献
9.
《Operations Research Letters》2021,49(5):650-654
In this paper, we study the busy-period distribution for discrete-time queues assuming a Bernoulli arrival process, with arbitrary service-time and batch-arrival distributions. We derive explicit analytic formulas for these distributions using the Lagrange Implicit Function Theorem applied to probability generating functions. The convenient coefficient operator notation used in these formulas leads to a computationally efficient method for obtaining the distributions in their entirety from these analytic formulas. 相似文献
10.
In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280]. 相似文献
11.
L. G. Kurakin 《Mathematical Notes》1998,63(4):503-508
Stability criteria of boundary equilibria for dynamical systems in the three critical cases, (n, k)=(3, 0), (2, 1), and (1, 1), are obtained.Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 572–578, April, 1998.The author wishes to thank V. I. Yudovich for useful discussions.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01791 and by the International Science Foundation under grant NRQ000. 相似文献
12.
Soon-Mo Jung 《数学学报(英文版)》2010,26(11):2085-2092
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g(x, y) + h(x, y)y' =0. 相似文献
13.
Steven G. Krantz Harold R. Parks 《Journal of Mathematical Analysis and Applications》2008,340(2):1263-1270
The classical Lagrange inversion theorem is a concrete, explicit form of the implicit function theorem for real analytic functions. An explicit construction shows that the formula is not true for all merely smooth functions. The authors modify the Lagrange formula by replacing the smooth function by its Maclaurin polynomials. The resulting modified Lagrange series is, in analogy to the Maclaurin polynomials, an approximation to the solution function accurate to o(xN) as x→0. 相似文献
14.
L. Kuntz 《Journal of Optimization Theory and Applications》1995,86(1):263-270
A new implicit function theorem for a class of nonsmooth functions is proved. It is used to improve the directional implicit function theorem of Demidova and Demyanov (Ref. 1). 相似文献
15.
Let F be an algebraically closed field of characteristic 0, and let f : F
n
→ F. We show that f is implicitly definable by a system of polynomial equations if and only if f is a special kind of piecewise rational function. 相似文献
16.
Liang-Chung Hsia Julie Tzu-Yueh Wang 《Transactions of the American Mathematical Society》2004,356(7):2871-2887
We generalize the ABC theorems to the function field of a variety over an algebraically closed field of arbitrary characteristic which is non-singular in codimension one. We also obtain an upper bound for the minimal order sequence of Wronskians over such function fields of positive characteristic.
17.
T. P. Lukashenko 《Mathematical Notes》2000,67(1):69-80
For arbitrary function systems, the growth of partial sums is estimated depending on the growth of the corresponding Lebesgue
functions. We prove analogs of the Kolmogorov-Seliverstov-Plessner convergence theorem for trigonometric series and the Kaczmarz
convergence theorem for orthogonal series for arbitrary (nonorthogonal) function systems as well as for orthogonal-like and
generalized orthogonal-like systems.
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 87–101, January, 2000. 相似文献
18.
A. F. Izmailov 《Mathematical Notes》2000,67(1):45-54
We derive a result on local representations of a nonlinear mapping family in a neighborhood of a 2-regular singularity. Theorems
of this kind are special forms of implicit function theorems and contain many very important results of local nonlinear analysis.
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 57–68, January, 2000. 相似文献
19.
We prove an existence theorem for , , in , using the shooting method. The function is supposed to be asymptotically linear.