Sentence examples for continuation proved from inspiring English sources

Even though the present study design did not expressly provide for any follow-up and no data are therefore available to substantiate the authors' claim, they do have good reasons to believe that with regard to a number of former study subjects the obvious benefits of continuation proved a persuasive enough argument.

By using bifurcation theory and the continuation method, they proved the following.

Using Mawhin's continuation theorem, the author proved that Eq. (1.1) has at least one T-periodic solution.

By applying the Manásevich-Mawhin continuation theorem, the authors proved that equation (1.2) has at least one positive T-periodic solution.

For ImQ is isomorphic to KerL, there exists an isomorphism J N L : Im Q → Ker L. Then we shall give the coincidence degree continuation theorem, which is proved in [21].

where P ( x ; D ) u = ∑ i, j = 1 n a i j ∂ 2 u ∂ x i ∂ x j + A u + ∑ k = 1 n A k ∂ u ∂ x k, here a ij are real numbers, A = A (x), A k = A k (x) and V (x) are the possible linear operators in a Banach space E. Jerison and Kenig started the theory of L p Carleman estimates for Laplace operator with potential and proved unique continuation results for elliptic constant coefficient operators in [1].

It's the continuation of what proves to be a long and fruitful partnership between Affleck and Warner Bros.

Next, applying the Manśevich Mawhin continuation theorem, we prove the following theorems.

(1.3) and used Mawhin's continuation theorem to prove the existence result.

By means of the Manásevich-Mawhin continuation theorem, we prove that (1.3) has at least one positive T-periodic solution.

By applying Mawhin's continuation theorem, we prove that the given equation has at least one positive T-periodic solution.