There is a fairly standard existence monist and nihilist reply to arguments in the vicinity of 1 3, which involves attempts to paraphrase claims of commonsense.
According to the standard existence theory for ordinary differential equations there exists a continuous solution of this system, on some interval.
end{aligned} end{aligned} (13) Since the square root function is not Lipschitz continuous near 0, we cannot apply standard existence theorems to obtain a solution to (13) with the full multiplicative noise term.
(1.4) Actually, standard existence and uniqueness results follows from a similar process in Theorem 1.1 in [21].
The right-hand side of (7) is a Lipschitzian function with respect to φ, hence the standard existence, uniqueness, and continuous dependence on the initial data theory applies to this equation, and these results carry over via (6) to (2) and (1).
Proof By the standard existence theorem for ODEs, it follows that system (3.3) possesses a local solution ( u ˜ ( t ), v ( t ), ψ ˜ ( t ) ) ∈ C ( 0, T ; E ), where [ 0, T max ) is the maximal interval of existence of the solution of (3.3). Now, we prove that this local solution is a global solution.
By standard existence theory [32 34], it is easy to establish the local existence of the unique solution ((u x,t), w x,t), v x,t),z x,t))) of model (2) for (xinoverline{Omega}) and (tin[0,T_{max}]), where (T_{max}) is the maximal existence time for solution of the model (2).
The study of problem (1) requires some care because, even if pairs of constant lower and upper solutions can easily be exhibited, the presence of the curvature term rules out in general the possibility of applying the standard existence results, due to the possible occurrence of derivative blow-up phenomena (see, e.g., [5]).
Perhaps if Common Core supporters want to silence their critics, they should start by informing more citizens about the Standards' existence.
Indeed, that there is a real standard of beauty (including moral beauty)—i.e., a standard with a real existence independent of human minds is perhaps the central idea of Shaftesbury's thought as a whole.
If the normative is first of all the normal, however, it might seem that talk about a norm for the singularity of existence, a standard for thinking about what is my ownmost just as I myself, would be incoherent.
