Showing papers in "Journal of Mathematical Analysis and Applications in 1974"

TL;DR: The variational principle states that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F'(uJj* < l, i.e., its derivative can be made arbitrarily small as discussed by the authors.

TL;DR: In this article, the authors apply a class of seminorms on X to obtain upper and lower bounds for certain families of solutions to (LDE) and apply these bounds to periodic linear equations, they are able to give estimates on the absolute values of the multipliers of LDE and also improve some of the bounds for linear equations obtained in Martin [5, Propositions 4 and 51.

TL;DR: In this article, it is shown that there is at most one solution of this problem, and a constructive quasireversibility method of constructing solutions of (1.1) which approximately satisfy the final condition.

TL;DR: In this paper, it was shown that a trajectory of (1) starting in Q at t = 0 lies entirely either in Q or on one of the positive semiaxes.

TL;DR: In this article, the n-body problem is formulated as a problem of functional analysis on a Hilbert space G whose elements are analytic functions of complex dynamical variables, and it is assumed that the two-body interaction is local and spherically symmetric.

TL;DR: In this article, it was shown that the core of a convex game behaves nicely, and a characterization of the extreme points of a finite game with infinite players was given, using a different method.

TL;DR: The stability and asymptotic behavior of solutions of an autonomous linear differential system x' =,4x are determined by the spectrum of the constant matrix A as discussed by the authors, which is the limiting system X' = Ax.

TL;DR: It is proved that the optimal controller for a discrete-time linear dynamic system with quadratic performance criterion is a linear function of the state variables when the additive random vector is a nonlinear function ofThe state and/or control variables.

TL;DR: In this paper, it was shown that f has no nontrivial T-periodic solution for the case of the vector retarded functional differential equation (VDFE) when the requirement upon the linear part is not satisfied.

TL;DR: In this paper, the authors develop a sufficient condition for continuity of the optimal set of a mathematical program, as opposed to upper semicontinuity, and apply it to the theory of economic choice.

TL;DR: The computational complexity of partitioning sparse matrices is developed graph-theoretically and the results are used to study tearing and modification, and to show that single-element tearing of symmetric systems is rarely advantageous when the torn system is solved by elimination.

TL;DR: In this paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations, and the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions and essentially bounded functions.

TL;DR: In this article, the authors studied the nonlinear boundary value problem for n-dimensional vector functions and obtained results analogous to those for the scalar case, by transforming the appropriate differential equation into a canonical or diagonalized system of two first-order equations.

TL;DR: In this article, a class of continous time nonlinear programming problems relating to problems of acquisition, stockpiling and distribution of materials is considered, where nonlinearity appears in both the objective function and the constraints.

TL;DR: In this article, the authors further extend these results to obtain many results on when projection formulas of the above types hold for the discrete orthogonal polynomials of Hahn, Krawtchouk, Meixner, and Charlier.

TL;DR: In this paper, the existence and uniqueness theorems for mild solutions of the Riccati equation with unbounded operators are established using a sequential approach based on approximating controllers for the linear quadratic cost control problem.

TL;DR: In this paper, the authors examined strong additivity, absolute continuity, and compactness in the space of vector measures and discussed various relationships among these concepts, even in the scalar case.