Strong Squeezing Property

Abstract

Let u _i ,(t) = S(t)u ^o _i , i = 1, 2, be two solutions of (2.1). Then their difference w = u₁(t) − u₂(t) satisfies the equation

$$ \frac{d}{w} + \rlap{--}{\lambda}\left( t \right)w = 0 ,$$

((4.1))

$$w\left( 0 \right) = {w_0} = u_1^0 - u_2^0,$$

((4.2))

where

$$ \begin{gathered} \rlap{--}{\lambda}\left( t \right)g = Ag + Cg + B\left( {u\left( t \right),g} \right) + B\left( {g,u\left( t \right)} \right), \hfill \\ u\left( t \right) = \frac{1}{2}\left( {{{u}_{1}}\left( t \right) + {{u}_{2}}\left( t \right)} \right) \hfill \\ \end{gathered} $$

((4.3))

.