Sentence examples for a solution provided from inspiring English sources

Then problem (1.10), (7), (8) has a solution provided that  .

Hence the linear problem (16) with nonlinear impulses (2) has a solution provided that (7) holds.

However, Hartshorne sees in Plato's myth the elements of a solution, provided the demiurge and the world-soul are not separate deities, but aspects of the same deity.

Then, the common fixed point problem CFP f, g, E) has a solution provided that f is order continuous and g is a dominated map.

Then, the common fixed point problem CFP f, g, K) has a solution provided that f is continuous and g is a dominated map.

First we consider (1.2) as a perturbation of the nonlocal system and prove that if and grow linearly, then (1.2) has a solution provided is not too large.

Of course such a solution provides a unique possiblerepresentative of the running time.

Therefore, security, software and cloud systems are likely to be as important in a networking solution provided to a customer as a network switch or a router.

According to Theorem 4.4, problem (5.1) admits a mild solution, provided that (4.1) holds.

Applying Theorem 3.1, we can find that (3.29) has a unique solution provided.

Then the problem (1.2) does not admit a nonconstant solution provided that frac{1}{d}>frac{8a}{5}-frac{25}{a }>frac{8a}{5}-frac{25}{a