Then, (a) the problem (4.1) for and with sufficiently large has a unique solution that belongs to and the following coercive uniform estimate holds: (4.8) . the problem (4.1) for and with sufficiently large has a unique solution that belongs to and the following coercive uniform estimate holds: (4.8).
Then there is b ∈ ( 0, b 0 ] such that the problem (26) has a unique solution that belongs to the space W p 2 ( 0, b ; E ( A ), E ).
We are going to show that equation (1.1) has a positive solution that belongs to space (C_(I =C [0,1]; mathbb{R}_)).
Then, (a for all, for and sufficiently large, the problem (7.1) has a unique solution that belongs to the space and the following coercive estimate holds: (7.5).
TCP-DAA [54] is another solution that belongs to the category of generating a delayed ACK, which generates an ACK according to the channel conditions.
Recall that, in (mathbb{R}^{N}), with any (N ge2), we are restricted to a class of radially symmetric solutions that belong to the space H denoted by (1.7) and for which we know their exponential decay at infinity.
(1.9) In particular, radial solutions that belong to the space H denoted by (1.7).
for f ∈ L p 1 and for sufficiently large μ, have unique solutions that belong to W p 1 l , and the coercive estimates hold ∥ u ∥ W p 1 l ≤ C ∥ ( A ˆ + μ ) u ∥ L p 1 , ∥ u ∥ W p 1 2 m ≤ C ∥ ( D β A ˆ + μ ) u ∥ L p 1. for solutions of problems (5.4) and (5.5).
Then, for f ∈ L p ( G ; E ), | arg λ | ≤ φ and sufficiently large | λ |, problem (24) has a unique solution u that belongs to W p, α [ 2 m ] ( G ; E ( A ), E ) and the following coercive uniform estimate holds: ∑ k = 1 n ∑ i = 0 2 m | λ | 1 − i 2 m t k σ k i ∥ D x k [ i ] u ∥ L p ( G ; E ) + ∥ A u ∥ L p ( G ; E ) ≤ C ∥ f ∥ L p ( G ; E ). (25).
where b > a ≥ 0. The purpose of this section is to present an existence theorem for a solution to (3.1) that belongs to X = C [ a, b ] (the set of continuous real functions defined on [ a, b ] ) by using the obtained result in Corollary 2.4.
