6,374 research outputs found
Existence of non-oscillatory solutions of a kind of first-order neutral differential equation
This paper deals with the existence of non-oscillatory solutions to a kind of
first-order neutral equations having both delay and advance terms. The new results are established using the Banach contraction principle
Differential equations of electrodiffusion: constant field solutions, uniqueness, and new formulas of Goldman-Hodgkin-Katz type
The equations governing one-dimensional, steady-state electrodiffusion are
considered when there are arbitrarily many mobile ionic species present, in any
number of valence classes, possibly also with a uniform distribution of fixed
charges. Exact constant field solutions and new formulas of
Goldman-Hodgkin-Katz type are found. All of these formulas are exact, unlike
the usual approximate ones. Corresponding boundary conditions on the ionic
concentrations are identified. The question of uniqueness of constant field
solutions with such boundary conditions is considered, and is re-posed in terms
of an autonomous ordinary differential equation of order for the electric
field, where is the number of valence classes. When there are no fixed
charges, the equation can be integrated once to give the non-autonomous
equation of order considered previously in the literature including, in the
case , the form of Painlev\'e's second equation considered first in the
context of electrodiffusion by one of us. When , the new equation is a
form of Li\'enard's equation. Uniqueness of the constant field solution is
established in this case.Comment: 29 pages, 5 figure
Principal-Agent Problem with Common Agency without Communication
In this paper, we consider a problem of contract theory in which several
Principals hire a common Agent and we study the model in the continuous time
setting. We show that optimal contracts should satisfy some equilibrium
conditions and we reduce the optimisation problem of the Principals to a system
of coupled Hamilton-Jacobi-Bellman (HJB) equations. We provide conditions
ensuring that for risk-neutral Principals, the system of coupled HJB equations
admits a solution. Further, we apply our study in a more specific
linear-quadratic model where two interacting Principals hire one common Agent.
In this continuous time model, we extend the result of Bernheim and Whinston
(1986) in which the authors compare the optimal effort of the Agent in a
non-cooperative Principals model and that in the aggregate model, by showing
that these two optimisations coincide only in the first best case. We also
study the sensibility of the optimal effort and the optimal remunerations with
respect to appetence parameters and the correlation between the projects
Asymptotic Properties of Solutions of Two Dimensional Neutral Difference Systems
In this paper we obtain sufficient conditions for the asymptotic properties of solutions of two dimensional neutral difference systems. Our result extends some existing results in the literature. An example is given to illustrate the result
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