Sentence examples for exists a classical from inspiring English sources

It is found that under the second-order approximation, there exists a classical type of relative equilibria except when the rigid body is near the surface of the central body and the central body is very elongated.

(c) If (varphi, z in D(A_{0})), and f̃ satisfies the local Lipschitz condition (5.6), then there exists a classical solution of (5.7 - 5.9) given by (5.5).  .

If (varphi, z in D(A_{0})), and f̃ satisfies the local Lipschitz condition (5.6), then there exists a classical solution of (5.7 - 5.9) given by (5.5).

For a classical mixture of two pure states (e.g., water and oil), the pure states are disjoint if and only if there exists a classical observable such that the expectation values with respect to these states are different.

Under these assumptions, the classical parabolic equation theory ensures that there exists a unique classical solution (u x,t)) for problem (1.1) with some (T>0) and the solution is positive over (overline{D}times[0,T)). Moreover, by regularity theorem [1], (uin C^{3}(Dtimes(0,T))C^{3}^{2}(overline{D}times[0,T))).

From [29, Theorem  5.3.4], we conclude that (1.3) exists a unique classical solution satisfying (3.1).

According to the mountain-pass Theorem 9, together with Lemmas 11 and 7, we deduce that there exists a nonzero classical solution of the problem (P).

Huang et al. [15] showed that for the 3D Cauchy problem there exists a unique classical solution in the case when the initial total energy is small, but there possible are large oscillations and a vacuum.

In [5 9], the authors proved there exists a direct (classical or mild) solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation, by which the optimal feedback law is obtained.

Similarly, we can show that there exists a nonnegative classical solution ( u 3, v 3 ) of (2.18) for ( x, t ) ∈ B 1 × ( 0, T ′ ), where T ′ denotes the maximal existence time.

and let S B denote the set of values (U, V) for which there exists a bounded, positive, classical solution f1of (2.8)-(2.10).