Sentence examples for autonomous cases from inspiring English sources

With this respect, see the introduction in [8], where different eventually autonomous cases are listed for related NLSEs arising in nonlinear optics.

Over finite dimensional spaces, the uniform exponential stability of the Cauchy problem ((Lambda_{n}, gamma, theta_{0})) in discrete and continuous autonomous cases has been investigated in [20, 23].

The similar skew-symmetric structure is extended from the autonomous case to the non-autonomous case.

In the next theorem we consider the autonomous case.

Necessary and sufficient conditions for the permanence of the autonomous case of (1.1) with two-species.

In [13], Zhang, Wu and Lu have proved this theorem in the autonomous case.

Note that an autonomous case of (1.1) was studied in [7].

First, stochastic stability of the underlying systems in the autonomous case is discussed.

The results obtained in this paper are still new even for the autonomous case.

The attractor of stochastic lattice FitzHugh-Nagumo system has been investigated in [4, 14, 15] in the autonomous case.

Kalantarov and Titi [11] studied a global attractor of a semigroup generated by equation (1.1) for the autonomous case.