A topological property of the solution funnel of x'=f(t,x), x(0)=x_0

Weigel, Herbert

facul_01; 8

Abstract:
The solution set S of an initial value problem
of an ODE of the first order was proved
by Hukuhara to be a connected subset in the space
of continuous functions, provided f is
bounded and continuous. While S is not path connected
in general, S has this property under the
additional assumption that f is quasimonotone, as is
shown in the present paper.

Primary MSC: 34A34 Nonlinear equations and systems, general, 34A40 Differential inequalities
Keywords: solution funnel, quasimonotone path connectedness
Notes:
The paper will appear in Nonlinear Analysis