Sentence examples for using the comparison principle from inspiring English sources

Some sufficient criteria have been given ensuring existence, uniqueness and global exponential stability of periodic solution of a class of recurrent neural network (RNN) model by using the comparison principle, the theory of monotone flow and monotone operator.

For each class of activation functions, testable algebraic criteria for ascertaining global exponential periodicity and global exponential stability of a class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator.

Again by using the comparison principle, we obtain the global existence of u x, t).

Remark 4.1 We can also easily reach our conclusion by using the comparison principle.

By using the comparison principle and inequality techniques some weaker conservative conditions are derived.

Using the comparison principle of the ODEs yields (f(t)leq F t)), for all (t>0).

This (piecewise) Markovian structure allows us to use the comparison principle of PDE, rather than the partial comparison of PPDE.

Use the comparison principle, then lim_{t to+infty} max_{xin[0,lpi]}u x,t leq1.

Our first observation is that, since we are utilizing PDE results, we can use the comparison principle for viscosity solutions of PDE directly.

Then using again the comparison principle yields w ( x, t + ε ) ≥ w ( x, t ) in Ω × ( 0, T − ε ) for an arbitrarily small ε > 0. Hence z t ( x, t ) = ( D + 2 α z ) − 1 w t ( x, t ) ≥ 0 in Ω × ( 0, T ).

By (2.2), one can get frac{dR}{dt}leq R t) biggl[lambdavarphi(t) pbigl(R t) bigr -frac{nu }{3} bigr -frac{nu by the similar method as that of the proof of Theorem 2.2, and by use of the comparison principle, one can also prove that the zero steady state of (2.2) is globally stable if (nu >lambdabar{varphi}{.