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Far from my theory that this was my first asthma attack, I had been having regular mild asthma attacks for years that I had accepted.
This is an important point given that regular mild exercise is recommended for the general population.
Regular mild to moderate exercise seems to improve the maternal perception of fetal movements through different mechanisms affecting both the mothers and the fetuses.
You can do both fitness walking and casual walking trips, or even regular mild hiking.
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Then the problem (1.1) has a unique pseudo almost periodic ϵ-regular mild solution.
Under the conditions of Theorem 3.1 there exists an ϵ-regular mild solution u of the problem (1.1).
If the constant c is small enough then the problem (1.1) has a pseudo almost periodic ϵ-regular mild solution.
The main scope of this work is to provide sufficient condition to ensure the existence of a pseudo almost periodic ϵ-regular mild solution of (1.1).
The notion of ϵ-regular mild solution for abstract semilinear evolution equations was introduced by Arrieta and Carvalho in [24] (see also [25]) where a detailed discussion was presented considering the importance of these types of solutions.
By an ϵ-regular mild solution of (1.1) we understand a continuous function (u:mathbb{R}to X^{1}) such that (uin C mathbb{R},X^{1+epsilon})) and verifies u(t)=int_{-infty}^{t}e^{A t-s)}fbigl(s,u(s) bigr), ds, quA t-snmathbb{R}fbigl s
The main result of this work basically says that if (f t,cdot)) is an ϵ-regular map relative to the pair ((X^{1},X^{0})) and belongs to (operatorname{PAP}(X^{1+epsilon},X^{gamma epsilon)})) then we will have existence of a pseudo almost periodic ϵ-regular mild solution to (1.1).
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