content_image/300465.jpg content_image/300464.jpg content_image/300463.jpg content_image/300462.jpg
for s ∈ ( s$_{k}$$_{1}$$_{−}$$_{1}$, s$_{k}$$_{1}$$_{+2}$$_{E}$ ] . 

The bounded solutions φ$_{ζ}$ ( s ) = { φ ij ζ ( s ) } , φ$_{˜}$ $_{ζ}$( s ) = { φ ij ˜ ζ ( s ) } of (2.7) satisfy the relation 

<img src='content_image/300465.jpg'>

Therefore, for s ∈ ( s$_{k}$$_{1}$$_{−}$$_{1}$, s$_{k}$$_{1}$$_{+2}$$_{E}$ ] , we have that 

<img src='content_image/300464.jpg'>

Define the function v ( s ) = e λs ∥ φ$_{ζ}$ ( s ) − φ$_{˜}$ $_{ζ}$( s ) ∥ . The inequality (4.9) implies that v ( s ) ≤ β$_{1}$e λs$_{k}$$_{1}$$_{−}$$_{1}$ + β$_{2}$ϵ γ e λs + ∫ s s$_{k}$$_{1}$$_{−}$$_{1}$ dv ( τ ) dτ + ∑ s$_{k}$$_{1}$$_{−}$$_{1}$<s$_{k}$<s δdv ( s$_{k}$ ) , s ∈ ( s$_{k}$$_{1}$$_{−}$$_{1}$, s$_{k}$$_{1}$$_{−}$$_{1+2}$$_{E}$ ] . 

Making use of the Gronwall’s Lemma for piecewise continuous functions, one can obtain that 

<img src='content_image/300463.jpg'>

Since the inequality (1 + δd ) i (( a$_{0}$,b$_{0}$ $^{))}$e d ( b$_{0}$ − a$_{0}$ ) ≤ (1 + δd ) $^{p}$e ( λ − α )( b$_{0}$ − a$_{0}$ ) is valid for any real numbers a$_{0}$ and b$_{0}$ with b$_{0}$ > a$_{0}$, we have 

<img src='content_image/300462.jpg'>

