Global Inverse Theorem Research Articles

The periodic boundary value problem for semilinear elastic beam equations: The resonance case

This paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition. The argument presented makes use of the global inverse theorem and Galerkin’s method.

Global homeomorphisms and covering projections on metric spaces

For a large class of metric spaces with nice local structure, which includes Banach?Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We first obtain a general condition in terms of a path continuation property. As a consequence, we deduce several conditions in terms of path- liftings involving a generalized derivative, and in particular we obtain an extension of Hadamard global inversion theorem in this context. Next we prove that, in the case of quasi-isometric mappings, some of these sufficient conditions are also necessary. Finally, we give an application to the existence of global implicit functions.

A global Inverse Map Theorem and biLipschitz maps in the Heisenberg group

We prove a global Inverse Map Theorem for a map f from the Heisenberg group into itself, provided the Pansu differential of f is continuous, non singular and satisfies some growth conditions at infinity. An estimate for the Lipschitz constant (with respect to the Carnot–Caratheodory distance in $\mathbb{H}$ ) of a continuously Pansu differentiable map is included. This gives a characterization of (continuously Pansu differentiable) globally biLipscitz deformations of $\mathbb{H}$ in term of a pointwise estimate of their differential. Keywords: Inverse problem, Heisenberg group

Global inversion theorems via coercive functionals on metric spaces

Let X and Y be metric spaces. We give sufficient metric conditions for a local homeomorphism f : X → Y to be a global one. We achieve this by means of auxiliary coercive functionals; several expected global inversion theorems are obtained by choosing different functionals.

A note on existence, uniqueness and continuous dependence for a non-linear heat conduction problem

Using the Levy-Caccioppoli global inversion theorem, a result of existence, uniqueness and continuous dependence is proved for a non-linear problem of heat conduction.

Atoms and regularity for measures in a partially defined free convolution semigroup

Consider a Borel probability measure μ on the real line, and denote by {μt : t≥1} the free additive convolution semigroup defined by Nica and Speicher. We show that the singular part of μt is purely atomic and the density of μt is locally analytic, provided that t > 1. The main ingredient is a global inversion theorem for analytic functions on a half plane.

Global inversion theorem to unique solvability of Dirichlet problems

Banach–Mazur–Caccioppoli global inversion theorem is applied to obtain a generalization of a result due to Ambrosetti and Prodi concerning unique solvability of a Dirichlet problem for a second-order differential equation.

Global invertibility of expanding maps

We prove a global inversion theorem in reflexive Banach spaces utilizing a recent generalization of the interior mapping theorem. As a corollary, we provide, under a mild approximation property, a positive answer to an open problem that was stated by Nirenberg. We also establish global invertibility of an α \alpha -expanding Fréchet differentiable map in Banach space under the assumption that the logarithmic norm of the derivative is negative.

A global inverse theorem on simultaneous approximation by Bernstein-Durrmeyer operators

We prove a global inverse result for simultaneous approximation by modified Bernstein operators as introduced by Durrmeyer in 1967. The main result of this note supplements and extends an earlier direct theorem of Heilmann and Müller and is given in terms of the so-called Ditzian-Totik modulus of second order.

Global univalence and global inversion theorems in Banach spaces

On etablit de nouveaux theoremes d'inversion globaux. On obtient des variantes globales du theoreme des fonctions implicite. On demontre une generalisation du theoreme de Hurwitz sur des suites de fonctions analytiques univalentes

An application of Hadamard-Lévy’s theorem to a scalar initial value problem

A global inversion theorem due to Hadamard and Lévy is applied to a Volterra integral operator acting in a space of continuous functions to obtain a one-sided criterion for global existence and uniqueness of a scalar initial value problem.

Global Surjection and Global Inverse Mapping Theorems in Banach Spaces

Global Surjection and Global Inverse Mapping Theorems in Banach Spaces

A note on global inversion theorems and applications to differential equations

Analysing the proof of Plastock’s theorem given by M. and S. RBdulescu [4] we prove that for 1; &/o(s) < cx, we may obtain estimates of the balls on which diffeomorphisms take place. Secondly, we shall use these results to find estimates for the existence interval of the solution of Cauchy’s problem for differential equation. These results will generalize a theorem of M. and S. Radulescu [3]. Throughout this paper E, F, G will denote Banach spaces.

Global inversion theorems and applications to differential equations

Global inversion theorems and applications to differential equations

A global inverse theorem for combinations of Bernstein polynomials

A global inverse theorem for combinations of Bernstein polynomials

Globally reciprocal stationary systems

This paper considers reciprocal stationary systems. By requiring a strict convexity condition (condition (C) in the text), we can prove that six generic representations are globally equivalent. The key is the global inversion theorem of Palais. Examples are given in electric circuits and thermodynamic systems. Relations to geometric formulations are indicated. Cet article considère des systèmes stationnaires réciproques. En exigeant une stricte condition de convexité (condition (C) dans le texte), nous pouvons prouver que six représentations génériques sont globalement équivalentes. La clé est le theorème de Palais sur l'inversion globale. Des exemples sont donnés en circuits électriques et en systèmes thermodynamiques. Les relations avec les formulations géométriques sont indiquées. Diese Arbeit untersucht reziproke stationäre Systeme. Indem wir eine strenge Wölbungsbedingung fordern (Bedingung (C) im Text), können wir beweisen, dass sechs generische Darstellungen global gleichwertig sind. Der Schlüssel liegt im globalen Inversionstheorem von Palais. Beispiele in elektrischen Schaltkreisen und thermodynamischen Systemen werden gegeben. Beziehungen zu geometrischen Formulierungen werden angedeutet. In questo articolo si trattano i sistemi stazionari reciproci. Richiedendo una condizione severa di convessità (condizione (C) nel testo), possiamo dimostrare che sei rappresentazioni generiche sono globalment equivalenti. La chiave à il teorema d'inversione globale di Palais. Si danno esempi nei circuiti elettrici e nei sistemi termodinamici. Si indicano rapporti con le formule geometriche. Paccмoтpeны взaимныe cтaциoнapныe cиcтeмы. Пpи нaлoжeнии жecткoгo ucлoвия выпuклocти (ucлoвиe c в paбoтe) мoжнo дaть дoкaзaтeльcтвo глoбaльнoй зквивaлeнтнocти для 6 poдoвыч пpeдcтaвлeний. Пpи зтoм вaжнa Пaлзoвcкaя тeopeмa глoбaльнoгo пpeвpaщeния. Дaютcя пpимepы в злeктpичecкич цeпяч и тepмoдинaмичecкич cиcтeмaч. Пoкaзaны cвязи c гeoмeтpичecкими фopмuляциями.

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

One parameter operator imbedding to modify Newton method for solution of nonlinear equations