Comparison theorem of the Hartman type for a continuous family of non-linear differential equations of the form p(t, λ)ϕ(u ′) for s = 0 and ϕ(0) = 0, is proved with the help of the generalized Mingarelli's identity.

and Applied Analysis 3 moreover we summarize some properties of a Hartman-type function. Lemma 4 (see [8]). LetG : I×I → R be the function defined as follows: as 0 ≤ t < η, G (t, τ) = { { { { { { { { { {

The purpose of this note is to extend the recent generalized version Grobman-Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation a linear dynamics admits exponential dichotomy topologically conjugated its part. In addition, under certain mild additional conditions, conjugacy in fa...

In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

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