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The generic g-property for a class of NFDE's by Jose C.F. DeOliveira is a Mathematics article available to read on EtoBox.

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We are concerned here with hyperbolic equilibrium points of nonlinear autonomous neutral functional differential equations (NFDE). Our main result consists in proving that, in a Baire metric space &r whose elements are NFDE's, the subset of equations which admit only equilibrium points of hyperbolic type is residual in f. l. DEFINITIONS AND STATEMENT OF RESULTS ## We follow the notation and terminology introduced by Hale [1]. Let us fix a nonnegative real number r and a n-dimensional vector space E ~ with norm ] • I. Let C be the space of continuous functions ~/, from [--r, 0] into E ~, endowed with the uniform norm [6 1 ~ max{] ¢(0)I : --r ~ 0 ~ 0}. For any continuous function x: I -+ E n, I C ~ an interval, and any t ~ I v~ (I + r), we denote by x, the element of C given by xt(O) = x(t -~ ~), --r ~ ~ ~ O. An autonomous functional differenti M equation is a relation of the form d d-t D(x,) = f(x,), (1) where D and f are continuous functions from C into E ~. If D is continuously differentiable on an open Set f2 C C and, for any 6 6 sQ, D'(~) is atomic at zero, according to the definition below, we say that (1) is a neutral functional differential equation on [2.

Who reads The generic g-property for a class of NFDE's?

Author

Jose C.F. DeOliveira

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-0396)

Published

1979

Language

EN

Field

Mathematics (Physical Sciences)