This show that, for small enough, there exists an unique fixed point on and only depends on.
Since w ( y ) = 0, we deduce from the upper semicontinuity of w that lim ε → 0 sup { w ( x ) : x ∈ B ( y, ε ) ∩ Ω ¯ } ≤ 0. Given ε > 0 small enough, there exists i ε large enough such that x i ∈ B ( y, ε ) ∩ Ω ¯ for i ≥ i ε.
It is well known that when antenna spacing (AS) among elements is not large enough, there exists mutual coupling among the elements and their patterns are changed.
In order to prove this fact, we show that for every positive integer k, when a suitable parameter is large enough, there exists a solution which presents k peaks.
end{aligned} Since (p< q< p^), taking (rho >0) small enough, there exists a (beta_{lambda }>0) such that (J_{lambda } u geq beta_{lambda }) for (Vert uVert _{lambda V}=rho_{lambda }).
When k is large enough, there exists a constant (delta>0) such that (|u_{k}(x)|<delta/2). Then (g x,u_{k}(x))=widehat{g} x,u_{k}(x))).
Then, for k small enough, there exists a unique solution pair ((u^{hk},v^{hk})in(S_{hm}(Omega)otimes P_{l}(J_{n}))^{2}) to the system of equation (2.10 - 2.11).
It shows that if the coding field is big enough, there exists a linear network MDS code with minimum distance dmin = C − k + 1 where kis the dimension of the information transmitted in the source.
We will show that, for any t small enough, there exists an element (r(t)) such that (|r(t)|=o(t^{2})) and (r(t) inPhi(r(t))), i.e., (r(t)) is a fixed point of the mapping Φ.
Indeed, let x ( t ) = x ( t 0, φ 0 ) ( t ) and y ( t ) = y ( t 0, φ 0 ) ( t ) be two solutions of (3.1) and (ii -differentiable, we have: for h > 0 small enough, there exii -differentiableifferences x ( t − h ) ⊖ x ( t ), y ( t − h ) ⊖ y ( t ).
Then, if ξ ( t ), ψ ( t ) are any (ii -solutions of FFDE (3.1) such that ξ 0, ψ 0 ∈ C σ exii -solutions +, we have D 0 [ ξ ( t ), ψ ( t ) ] ≤ r ( t, t 0, u 0 ), profided that D σ [ ξ 0, ψ 0 ] ≤ u 0. ProoFFDEnce ξ, ψ are solutions of FFDE (3.1) and [(ii)-gH]-differentiable, we have: for h > 0 suchl enough, thate exist the Hukuhara differences ξ ( t − h ) ⊖ ξ ( t ), ψ ( t − h ) ⊖ ψ ( t ).
