Sentence examples for the following continuation from inspiring English sources

As a key tool, we need the following continuation result on pseudomonotone operators, which follows from the homotopy invariance of the above degree.

The given information is necessary for the following continuation theorem.

Similarly to Theorem 5.1, we can prove the following continuation principles using Theorems 4.1 and 4.6, respectively.

The following continuation theorem of coincidence degree theory is crucial in the arguments of our main results.

The proof of the main result (cf. Theorem 5.1 below) will be based on the combination of a bound sets technique together with the following continuation principle developed in [16].

Next, we examined the risk for ApoE-induced atherosclerosis following continuation of high-fat diet treatment for a total of 25 weeks (Fig 1).

The following is continuation of experimental studies into CFRP anchorage systems used to retrofit concrete structures.

Moreover, we have the following unique continuation properties for the strong solution.

We prove the following analytic continuation theorem which applies to any virtual representation of any symmetric space (G, K, σ).

Similar to the proof of Theorem 3.1 [10] and Proposition 4.2 [12], one can prove the following unique continuation properties.

The existence of solutions of the Neumann and periodic boundary value problems of semilinear differential equations has been extensively studied by many authors via the following Mawhin continuation theorem (see [19 23] and references therein).