Sentence examples for using the continuation theorem from inspiring English sources

By using the continuation theorem of Mawhin's coincidence degree theory and some inequality techniques, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of neural networks with variable coefficients and time-varying delays.

By using the continuation theorem of Mawhin's coincidence degree theory and Gronwall's inequality, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of cellular neural networks with periodic coefficients and delays.

By using the continuation theorem of Mawhins coincidence degree theory and constructing a suitable Lyapunov function, some new sufficient conditions are obtained ensuring existence and global asymptotical stability of periodic solution of cellular neural networks with periodic coefficients and delays, which do not require the activation functions to be differentiable and monotone nondecreasing.

By using the continuation theorem of Mawhin's coincidence degree theory, Lyapunov functional method and some analytical techniques, some sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of the self-connection BAM neural networks with periodic coefficients and delays.

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique.

By using the continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, we derive some sufficient conditions for the existence and global exponential stability of a unique periodic solution of BAM neural networks, which assumes neither the monotony nor the boundedness of the activation functions.

To obtain the existence of positive ω -periodic solutions of system (2), we will use the continuation theorem.

Since ImQ is isomorphic to KerL, there exists an isomorphism J : Im Q → Ker L. In the proof of our existence theorem, we will use the continuation theorem of Gaines and Mawhin [8].

In fact, to use the continuation theorem, it suffices to prove that there exists a positive constant 0 < ε 0 ≪ 1 such that, for any possible solution ( x 1 ( t ), x 2 ( t ) ) of (2.2), the following condition holds: | x 2 ( t ) | < 1 − ε 0. (2.4).

In order to use the continuation theorem to study the positive T-periodic solutions for equation (1.5), we consider the following system: textstylebegin{cases}u^{(m)}(t)= [A^{-1}varphi_{q} v)](t), v^{(m)}(t)=-f(u(t))u'(t)-g(t,u(t-tA^{-1}varphi_{q} ves} (2.1) where (q>1) is a constant with (1/p+1/q=1).

Using the Manásevich Mawhin continuation theorem, we prove that the equation has at least one T-periodic solution.