Showing papers in "Journal of Differential Equations in 1977"

TL;DR: In this article, the authors consider the problem of finding a set-valued mapping from I into H such that the sets C(t) are nonempty closed and convex.

TL;DR: In this paper, it was shown that all singularities with characteristic orbits are topologically determined by a finite jet, and for each n, there are only a finite number of topological equivalence classes of codimension n singularities having characteristic orbits.

TL;DR: One of the simplest topological variations of the phase space of a one-parameter family of differential equations (vector fields, flows) is the creation of periodic orbits from equilibria as the parameter crosses a critical value as mentioned in this paper.

TL;DR: In this paper, the authors present a model of two species competing for a single resource and show that one of the two species must go extinct, which is an illustration of the principle of competitive exclusion.

TL;DR: In this paper, the existence and uniqueness of global solutions of (1.1)-(1.2) is studied in a real Hilbert space H. The method of proofs employed here is what is called the potential well method.

TL;DR: In this article, the existence of solutions for a class of linear functional differential equations defined on a general Banach space is established; the solutions are shown to generate a semigroup of class C0; a representation of the solutions in terms of a particular family of linear transformations is developed.

TL;DR: In this paper, the mixed problem for the system of equations wt u, = 0, uf + P(4, p 4, p 2v-y, y = 1 + 2~, E > 0, K = const > 0.

TL;DR: In this article, the authors consider limit points (when 1 t 1 + co) of the translatesf,, wheref, s, x, s = f(~, t + s).

TL;DR: By casing the conditions the author automatically improves many results, including the validity of the LaSalle invariance principle in stability for the nonautonomous system dx/dt = f(x,t).

TL;DR: The authors apply Lie algebraic methods of the type developed by Baker, Campbell, Hausdorff, and Zassenhaus to the initial value and eigenvalue problems for certain special classes of partial differential operators which have many important applications in the physical sciences.

TL;DR: In this article, it was shown that if F satisfies the hypothesis of Kamke type, then the closure of the set of solutions of problems 1 and 2 is the same as that of problems 2 and 3.