Sentence examples for ensures existence from inspiring English sources

Strong ellipticity of differential operators is a requirement that ensures existence of a unique solution.

This ensures existence of a laissez faire equilibrium.

This is the reason why the authors proposed the constraint below, which ensures existence of a minimum.

Hence the fundamental theorem of existence and uniqueness ensures existence and uniqueness of solution of the system (1.5) with the given initial conditions.

In the proof of the second a priori estimate, we obtained boundedness of similar integrals (5.14) by the use of the weight function y λ + 1 instead of y, which ensures existence and boundedness of the integrals.

Stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation.

We use advanced results from the calculus of variations to ensure existence of a solution and derive sufficient and necessary conditions for optimality.

By using exponential dichotomy, the Banach fixed point theory and some inequality analysis technology, some sufficient conditions are derived ensuring existence, uniqueness and global attractivity of almost periodic solution of delayed cellular neural networks (DCNNs) with time-varying coefficients.

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.

By using M-matrix theory, some inequality analysis technology and mathematical induction, some sufficient conditions are derived ensuring existence and global exponential stability of the equilibrium points of delayed cellular neural networks (DCNNS) with impulses.

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.