Results 221 to 230 of about 24,633 (266)

Existence and Uniqueness

2006
Abstract We begin this chapter by asking the reader to review Picard’s method introduced in Chapter 1, with particular reference to its application to Volterra equations. This done, we may fairly speedily reach the essential core of the theory of ordinary differential equations: existence and uniqueness theorems. To see that this work is
openaire   +1 more source

On the Existence and Uniqueness of General Equilibrium Prices

International Economic Review, 1984
There have recently been revived interests in the application of the theory of degree to existence and uniqueness problem of the general equilibrium. A crucial issue is how to deal with the excess demand function on the boundary of the price domain. Previous contributions in this field have employed assumptions that are different from one another.
openaire   +2 more sources

Existence and uniqueness of the solution

2010
The proof of the existence and uniqueness of the solution to problems (1.22), (1.20) and (1.24) is quite similar. In this chapter, followingAlonso Rodriguez et al. [11], we mainly focus on the magnetic boundary value problem (1.22), adding in Section 3.5 a few comments on the electric boundary value problem(1.20) and the no-flux boundary value problem (
Ana Alonso Rodríguez, Alberto Valli
openaire   +1 more source

Questions of existence and uniqueness

2017
This chapter discusses the fundamental existence and uniqueness questions in symplectic topology: which manifolds admit symplectic structures, and to what extent they are unique. There are partial answers for some classes of manifolds and many related open problems.
Dusa McDuff, Dietmar Salamon
openaire   +1 more source

Existence and Uniqueness Theorems

2010
In this chapter we are concerned with the first-order vector differential equation $$x^\prime = f(t, x).$$
Walter G. Kelley, Allan C. Peterson
openaire   +1 more source

Existence and Uniqueness of Solutions

1992
Recall the inhomogeneous system (I) of k linear equations in n unknowns, which we studied in Chapter 4.4. We consider the case k = n, where the number of equations to be solved equals the number of unknowns, and we shall use our results about bases in ℝ n in the preceding chapter to study the question of existence and uniqueness of solutions of the ...
Thomas Banchoff, John Wermer
openaire   +1 more source

Existence and Uniqueness Results

2014
This chapter deals with existence and uniqueness results for variational and quasi-variational inequalities. With the intention of focusing the differences among the proofs of results, we first consider elliptic variational inequalities of the first and second kind with linear and continuous operators in Hilbert space or monotone and hemicontinuous ...
openaire   +1 more source

Stability, existence and uniqueness

2009
Abstract This chapter develops the stability theory needed for the existence of the classical partition. This is extended to quantum stability with emphasis on the physically important case of nonrelativistic quantum mechanics with Coulomb interactions. The existence and uniqueness of the thermodynamic limit is discussed in detail.
openaire   +1 more source

Existence and Uniqueness of Solutions

1968
In Chapter 6 we have repeatedly postponed an investigation of the existence and uniqueness of the current chains and voltage chains describing the performance of a resistive network, but subject to the restrictions imposed by Ohm’s Law and Kirchhoff’s Current and Voltage Laws. In the first part of this Chapter we finally consider such matters.
openaire   +1 more source

Existence and Uniqueness of Solutions

2009
A fundamental issue in the theory of differential equations consists of proving the existence and uniqueness of solutions. Before we discuss partial differential equations, we analyse in Section 9.1 the situation for general systems of ordinary differential equations, often called differential algebraic equations.
openaire   +1 more source