Sentence examples for ensuring the existence from inspiring English sources

However, Theorem 1.6 is inapplicable in ensuring the existence of fixed points for the mapping in because there does not exist and satisfying the assumptions of Theorem 1.6.

Some new necessary and sufficient conditions are obtained ensuring the existence and uniqueness of periodic solutions.

Sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution are given.

Some new criteria ensuring the existence and uniqueness, and the global asymptotic stability (GAS) of equilibrium point are derived.

Higher education serves many purposes, from fostering individual growth and democratic values to ensuring the existence of a highly skilled work force.

"There is also a widespread understanding of the need to ensure that business can properly work under any new structure while ensuring the existence of certain protections".

We give sufficient conditions ensuring the existence of an almost automorphic solution when there is at least one bounded solution on R+.

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments.

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.

The resulting control problem is treated using a calculus of variation approach and conditions ensuring the existence of interior solutions are proposed.

By using Banach fixed point theorem and applying inequality technique, we give some sufficient conditions ensuring the existence and globally exponential stability of almost periodic solution.