Sentence examples for by using differential inequality from inspiring English sources

The authors obtained the sufficient conditions which guarantee the permanence by using differential inequality theory.

First, by using differential inequality theory, we obtain the permanence and non-permanence of the system.

By using differential inequality technique, the new neural network is shown to be globally exponentially convergent to optimal solution.

For the general non-autonomous case, sufficient conditions which ensure the permanence and global stability of the system are obtained by using differential inequality theory.

In this paper, by using differential inequalities, we establish the conditions on the nonlinearities to guarantee that u ( x, t ) exists globally or blows up at some finite time, respectively.

Some sufficient conditions ensuring the existence and global attractivity of almost periodic solution are derived by employing Banach fixed point theory and using differential inequality technique.

Transient dynamics and population crashes of this system are analysed using differential inequalities.

The methods depend on using differential inequalities of Poincaré or logarithmic Sobolev type.

Recently, by using differential and integral inequalities, Xu et al. have studied attracting and invariant sets of functional differential systems [12, 13] and impulsive functional differential equations [14].

We find that it is difficult to study the existence of blow-up and global solutions of problem (1.1) by using the differential inequality technique in [1].

By using the differential inequality technique, they gave the upper and lower bounds for blow-up time when the blow-up of the solution occurred.