Showing papers in "Journal of Differential Equations in 1980"

TL;DR: In this article, the authors determine the curves in λ-space of bifurcation to "strange" attractors and relate this to hyperbolic subharmonic Bifurcations.

TL;DR: In this paper, a local theory of weak solutions of first-order nonlinear systems of conservation laws is presented, where the transonic small disturbance equation is an example of this class of systems.

TL;DR: In this article, the authors investigate the regularity at time t = 0 of the solutions of linear and semi-linear evolutions equations (including the Stokes and Navier-Stokes equations), and give necessary and sufficient conditions on the data for an arbitrary order of regularity.

TL;DR: In this article, the authors considered the problem of infinite delay equations and proved existence, uniqueness, and continuous dependence of solutions in the state space of a function with bounded delay and bounded retardation.

TL;DR: Theorem 2.1 in this paper shows that a diffeomorphism f of a compact riemannian manifold M is Anosov if and only if its tangent map has a non-degenerate Lyapunov quadratic function.

TL;DR: In this article, the authors give general necessary and sufficient conditions for completeness of generalized eigenfunctions associated with systems of linear autonomous retarded functional differential equations (FDE), in the Hilbert space R n × L 2 ([− h, 0], R n ), and also in the space C ([ − h, 0, R n ).

TL;DR: In this article, it was shown that the linear systems defined by Σi defined by x i : x i = A i x i + B i u i, i = 1, 2, and x i defined by considering trajectories modulo their controllable subspace are topologically equivalent if and only if they have the same Kronecker indices.

TL;DR: In this article, the exponential growth of solutions of the linearized equations is described by the Spectral Theorem applied to the induced linear flow on the tangent bundle, and it is shown that whenever these secondary spectra are disjoint then an invariant complementary bundle can be found.

TL;DR: In this article, the authors give sufficient conditions for a C1 flow on a compact manifold with boundary, M, to be weakly structurally stable, i.e., if the flow satisfies a quadratic external boundary condition, then it is possible to demand that the conjugacy preserve the boundary.

TL;DR: In this article, it has been shown that the Pontrjagin maximum principle can be used as an assumption on a closed-loop control to generate open-loop optimal controls.

TL;DR: In this article, it was shown that there is a range of values for b and r over which the boundary value problem has traveling wave front solutions for the Belousov-Zhabotinskii chemical reaction.

TL;DR: In this paper, the authors present a set of hypotheses for proving the existence of topologically non-degenerate (seminondegenerate) homoclinic and heteroclinics in real analytic Hamiltonian systems with two degrees of freedom.

TL;DR: In this paper, the authors present a Razumikhin-type extension of Wazewski's Principle, which is widely applicable to concrete examples, and also an extension of the method to RFDEs with a merely continuous right-hand side.

TL;DR: In this paper, the authors considered the problem of time-independent surfaces of prescribed mean curvature, and showed that no physical problem has been known involving time-dependent surfaces, except the still unsolved and even nonattacked corresponding hyperbolic problem.

TL;DR: In this paper, the existence of transversal homoclinic points in the collinear three-body problem, restricted and general, and in the planar circular restricted three body problem was proved.

TL;DR: In this paper, it was shown that for strongly monotone β, all solutions are asymptotically almost-periodic in the energy space, under weaker assumptions than those used by G. Prouse.

TL;DR: In this article, it has been shown that if a certain non-degeneracy (or, as we shall say, normality) condition is satisfied then the latter problem satisfies the hypotheses of the theorem of [l] and, therefore, it admits a regular synthesis of the optimal control.