Sentence examples for under appropriate assumptions from inspiring English sources

We also show that mild solutions can become strong and classical solutions under appropriate assumptions.

Under appropriate assumptions, the asymptotic bias and variance of the proposed estimators are obtained.

Under appropriate assumptions on f and h, we get that the equation has two positive solutions by using variational methods.

Using the concentration-compactness principle, Fan proved the existence of ground state solutions vanishing at infinity under appropriate assumptions.

It is shown that, under appropriate assumptions, the solution of the closed-loop system is uniformly ultimately bounded.

It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a unique solution of THVIP (1.6).

In particular, under appropriate assumptions, this theorem provides an approximation scheme to the unique solution of (1.1).

Then under some appropriate assumptions, the stabilization condition for the systems under pure impulsive control is given.

Under some appropriate assumptions, results on stochastic stability and stochastic stabilization are developed.

Under the appropriate assumptions, the distributions of the non-dimensional flow velocity can be obtained.

Still under certain appropriate assumptions about (V^0), we can ensure microhyperbolicity (for (m_B=0,1) only).