The Poincare-Miranda Theorem

Kulpa, Władysław

doi:10.2307/2975081

Cited by 70 publications

(69 citation statements)

References 1 publication

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“…Let similarly γ i γ ui + γ di . Now, subtracting each (9) to each (8) and using constraint (11) to substitute for μ(l, n), we get: μ(hi, o), ∀i ∈ I Using constraint (10) to substitute for μ(hi, o) and substituting (12) for μ(li, o), we finally get:…”

Section: Existence Of a Steady State For The Ode Systemmentioning

confidence: 99%

Existence and uniqueness of a steady state for an OTC market with several assets

Bélanger

Ndouné

2016

Math Finan Econ

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Section: Existence Of a Steady State For The Ode Systemmentioning

confidence: 99%

Existence and uniqueness of a steady state for an OTC market with several assets

Bélanger

Ndouné

2016

Math Finan Econ

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“…We will obtain such a solution by applying the Poincaré-Miranda theorem [17], which is an n-dimensional extension of Bolzano's theorem.…”

Section: Existence Of a One-dimensional Heteroclinic Orbitmentioning

confidence: 99%

Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System

Carmona¹,

Fernández-Sánchez²,

Teruel³

2008

SIAM J. Appl. Dyn. Syst.

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Abstract. The proof of the existence of a global connection in differential systems is generally a difficult task. Some authors use numerical techniques to show this existence, even in the case of continuous piecewise linear systems. In this paper we give an analytical proof of the existence of a reversible T-point heteroclinic cycle in a continuous piecewise linear version of the widely studied Michelson system. The principal ideas of this proof can be extended to other piecewise linear systems.

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“…We first recall the statement of the Poincaré-Miranda theorem in the twodimensional case (cf., e.g., [26,29]). …”

Section: A Shooting Approach and The Elastic Lemmasmentioning

confidence: 99%

Multiplicity results for a class of asymmetric weakly coupled systems of second-order ordinary differential equations

Dalbono

McKenna

2005

Bound Value Probl

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We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.

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The Poincare-Miranda Theorem

Cited by 70 publications

References 1 publication

Existence and uniqueness of a steady state for an OTC market with several assets

Existence and uniqueness of a steady state for an OTC market with several assets

Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System

Multiplicity results for a class of asymmetric weakly coupled systems of second-order ordinary differential equations

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