Showing papers in "Journal of Differential Equations in 1972"

TL;DR: In this article, the controllability of nonlinear systems described by the equation dx/dt - F(x,u) was discussed and it was shown that strong accessibility implies strong accessibility for a large class of manifolds including Euclidean spaces.

TL;DR: The controllability properties of systems which are described by an evolution equation in a Lie group are studied in this paper, where revelant Lie algebras induced by a right invariant system are singled out, and the basic properties of attainable sets are derived.

TL;DR: The notion of expansive homeomorphism was introduced in this article for metric spaces, where the homeomorphisms are invariant to the shift homeomorphic properties of the metric space. And the topological entropy h(4) is related to the periodic points of (5) by the formula

TL;DR: In this article, Leray-Schauder degree theory for mappings of the form I T with I the identity and T : cl i2 -+ X completely continuous is presented.

TL;DR: In this paper, a unified approach to Global and Local Cauchy problems on finite or infinite time intervals is presented, and existence and uniqueness theorem for Caratheodory systems and Lipschitz systems are derived.

TL;DR: In this article, the authors provide an overview of stochastic differential equations in which control variables occur in the drift coefficient. And they describe a saddle point in pure strategies, and a scheme for optimal stopping in N-person games with perfect observation.

TL;DR: The notion of pseudo-differential operators has grown in recent years out of attempt to obtain sharp a priori estimates for the solutions of the partial differential equations as mentioned in this paper. But their algebra is too restrictive for many purposes.

TL;DR: In this paper, the authors investigated the properties of compact operator-valued symbols and showed that compact operators of order 03 give rise to compact operators and may hence take the place of smoothing operators in their theory.

TL;DR: Theorem 3 as discussed by the authors generalizes the boundary conditions studied in dimension d = 1 by Keller [9] and Bebernes and Gaines [2] and generalizes their conditions.

TL;DR: In this paper, it was shown that the minimal closed symmetric operator T, determined by a formally self-adjoint linear ordinary differential operator L on an interval (a, b) is simple if L is regular or quasi regular at one end.

TL;DR: In this paper, the existence, uniqueness, and continuation of solutions to the initial value problem for neutral functional differential equations are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem.