Sentence examples for distinct pairs from inspiring English sources

It quickly became hard not to view the foursome in two distinct pairs.

Then has at least distinct pairs of nonzero critical points.

Consequently, BVP (1.5) possesses at least distinct pairs nontrivial solutions.

Therefore, by Lemma 2.4, (mathcal{J}) has at least m distinct pairs of critical points, so system (1.1) possesses at least m distinct pairs of nontrivial homoclinic solutions.

Then, problem (3.19) has at least distinct pairs of nontrivial classical solutions, that is, problem (1.1) has at least distinct pairs of nontrivial classical solutions.

Then J has at least n distinct pairs of nonzero critical points.

Then J possesses at least k distinct pairs of critical points.

Therefore, J has at least k distinct pairs of critical points.

Then Φ possesses at least m distinct pairs of critical points.

Then φ has at least j distinct pairs of critical points.

By Theorem 2.2, possesses at least distinct pairs of nontrivial critical points.