Showing papers in "Journal of Differential Equations in 1976"

TL;DR: In this article, sufficient conditions are given for the existence of an exponential dichotomy or equivalently an invariant splitting over invariant subsets of the base space of a translation flow.

TL;DR: In this article, the authors studied the orbit structure of a Hamiltonian system in a neighborhood of a trajectory which is doubly asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection of the stable and unstable manifolds of a critical point.

TL;DR: In this paper, it was shown that for delay differential equations and partial differential equations, any almost periodic solution has only finitely many rationally independent frequencies, thus extending results of Cartwright for ODE's.

TL;DR: In this article, it was shown that if f is a C 1 diffeomorphism that satisfies Axiom A and the strong transversality condition then it is structurally stable.

TL;DR: In this paper, the autonomous nonlinear functional differential equation x(t) = F(xt), t ⩾ 0, x0 = φ is studied as a semigroup of nonlinear operators in Lp function spaces.

TL;DR: In this article, a new method of constructing solutions to the Cauchy problem for nonlinear hyperbolic systems of conservation laws in one space dimension is introduced, which is called Lax [lo] method.

TL;DR: The existence of such periodic solutions for a wide class of functions f (x, t) has been shown by Nehari using an approach based upon the calculus of variations as mentioned in this paper. But their proof is quite different and involves only some qualitative results and an application of the PoincarC-Birkhoff twist theorem.

TL;DR: In this paper, the authors proposed a different approach, which was intro-intrinsic to the classical method of solution of the Riemann problem, which is based on the construction of the shock and wave curves of (1.1).

TL;DR: In this paper, it was shown that the set of all K-tuples of C-vector fields on the Cr+l n-dimensional separable manifold M (1 n2 + n) is open and dense.

TL;DR: In this article, the authors prove that the second-order scalar equation has an asymptotic representation for x. The proof uses only "advancedcalculus" methods and ideas.

TL;DR: In this paper, it was shown how particles can separate into subsystems between which the distances are asymptotic to constant multiples of time, and within which the mutual distances are at most of the order t 2 3.

TL;DR: In this paper, the existence of a subsolution 4 and of a supersolution # with 4 < # (that is, $(x) < #(x) for all x E 0) guarantees the presence of a minimal solution zs and a maximal solution li of the BVP (l), in the sense that every solution u of (1) with 4 ≤ u < 9 satisfies E < u < 22.

TL;DR: In this paper, a feedback stabilization of a linear hyperbolic boundary value control system is implemented, and the property of controllability of the control system yields the asymptotic stability of the feedback system.

TL;DR: In this paper, the positive invariance of closed sets for delay-differential equations has been studied in a complete real inner produce space, where R is the real line and CB denotes the set of functions continuous and bounded on (−∞, 0] to X, and for φ ∈ CB, the authors present a definition of ∥ φ∥ = sup{φ(s) | s ≤ 0}.

TL;DR: In this paper, the authors relax the Poincare-birkhoff twist theorem for periodic solutions of the second order scalar ODE and show that the problem of global existence of solutions can be solved with the removal of the sign condition.

TL;DR: For general 2 × 2 genuinely nonlinear conservation laws and isentropic gas dynamics equations, not necessarily convex, this paper proved uniqueness theorems of the Cauchy problem for piecewise continuous solutions with a finite number of centered rarefaction waves in each compact set.

TL;DR: In this paper, the saddle point property of the functional differential equation with finite retardation was shown to be saddle point invariant under some conditions, such as the existence of saddle points in the point spectrum of a holomorphic function.

TL;DR: In this article, a general class of electrical networks including transistors, vacuum tubes, and various other electronic devices are discussed and conditions under which the dynamics is the gradient of a real valued function with respect to a certain 2-tensor field which comes naturally from capacitors and inductors in a network.

TL;DR: In this article, the authors consider continuous flows on arbitrary 2-manifolds (separable metric, but not necessarily compact nor orientable and possibly with boundary) and show that two such flows are (topologically) equivalent if there is a homeomorphism of M onto M, which takes orbits of 4 onto orbits of +' preserving sense (but not necessarily parametrization).

TL;DR: In this article, the degeneracy of functional differential equations with constant coefficients was discussed and the conjecture that linear difference-differential equations are point-wise complete was presented in an earlier paper on controllability of delaydifferential systems.

TL;DR: In this article, the authors studied the solvability of a nonlinear functional equation f E (A + B)u, where A is a maximal monotone (possibly multivalued) mapping from a reflexive Banach space X to its dual X* and B: X-+ X* satisfies some hind of sign condition.

TL;DR: In this article, the dependence of scattering data for a perturbed wave equation on the perturbation was established, and the results hold for both acoustic and SchrBdinger wave equations.

TL;DR: In this paper, the perturbed functional differential equation x (t) = L(x t ) + h(t ) is considered with the assumption that h is Lipschitzian in W 1,∞.