Showing papers in "Journal of Differential Equations in 1973"

TL;DR: In this paper, the entropy rate admissibility criterion for solutions of hyperbolic conservation laws is numerically analyzed and the equivalence of this criterion and viscosity criterion is established for the single equation and the system of equations of one dimensional nonlinear elasticity.

TL;DR: In this paper, Woinowsky-Krieger et al. modify the model by introducing terms to account for the effects of internal (structural) and external damping, and show that as time tends to infinity, provided 6 is not large and negative, any solution of (1.1) converges in a suitable topology to an equilibrium position of the beam.

TL;DR: The line of trivial solutions of a Banach space is a bifurcation point as mentioned in this paper, where a neighborhood of (h(E), u(s), F has zeros not on %.

TL;DR: In this paper, it was shown that the set of all parabolic orbits form a smooth submanifold of the phase space and that the points asymptotic to the origin correspond to parabolic points.

TL;DR: In this paper, some fixed point theorems were developed and applied to the question of existence of nontrivial periodic solutions of nonlinear, autonomous functional differential equations, and the standard results of G. S. Jones and R. B. Grafton can be obtained by their methods, and they prove periodicity results for some equations, for instance a neutral functional differential equation.

TL;DR: In this article, it is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.

TL;DR: In this paper, the authors consider the case of a monotone Lyu$unov function (77 is strictly decreasing on every trajectory in the complement of K) and of a hybrid Bolt.

TL;DR: In this paper, it was shown that the set of continuous f is also meager (first category) in X in the scnsc of the Ba&e Category Theorem, where a solution z(*) of (I) will be a solution through us = (to, x0) if (2) is satisfied.

TL;DR: In this paper, a rigorous procedure is presented to demonstrate the existence of a family of invariant curves on which a mapping of this motion can be based, with the aid of a third integral of motion.

TL;DR: In this paper, the authors studied the problem of initial v&e problems with initial values of T > 0 and showed that these problems almost always occur in applications with T = 0.

TL;DR: The pathological behavior of the invariant set of bounded orbits for the differential equation f = -(%)' where z = x1 + ha is a complex variable was examined in this article.

TL;DR: Henrard as mentioned in this paper generalized Lyapunov's center theorem relative to the existence of families of periodic orbits emanating from an equilibrium to cases where a resonance occurs between two basic frequencies.

TL;DR: In this paper, a framework for studying changes in the structure of an isolated invariant set under perturbations of the flow is developed, which is first required to define the continuation of the isolated set as the flow changes.

TL;DR: In this paper, the authors present a point of view which allows one to interpret the solutions of a non-autonomous differential equation as a classical dynamical system, without assuming uniqueness of solutions of the initial value problem.

TL;DR: In this article, it was shown that the existence of bounded solutions under weaker assumptions on the smoothness condition of a(t) and absolute continuity of f(i) was not required.

TL;DR: In this paper, the Lagrange Multiplier Rule was used in function space to obtain necessary conditions for optimal control problems with general nor&car retarded systems, where the trajectories must satisfy function space terminal conditions such as ~(0) = {(S), 0 E PI - h, ti], 4 being some given function.

TL;DR: In this paper, the authors present uniqueness theorems for positive solutions of the semilinear second order elliptic boundary value problem (1) below with a nonnegative nonlinearity F(x, zu) which is monotonic and sublinear in w.r.t.

TL;DR: In this article, the existence of a nonnegative (positive) solution of nonlinear boundary problems is established and an extension of the maximum principle for solutions of higher order equations is also indicated.

TL;DR: In this paper, the authors extended Popov's algebraic theory of pointwise degenerate systems with one delay to the case of several outputs and two delays, and showed that the degeneracy set can be extended to a special class of strongly regular systems, to which the time optimal problem belongs.