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It is true that the presumption of law is that the majority of the court are right and that I am wrong, yet, in the face of this presumption, and the positiveness with which the views of the majority are asserted, I cannot yield my convictions the other way, which were never clearer or stronger in any case.
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Letting t → ∞, we get a contradiction with the positiveness of y 3. The remaining case y 3 ( t ) < 0 can be eliminated in a similar way using (6).
Proof In view of Lemma 2 we can assume without loss of generality that x n > 0, y n > 0 and w n > 0. Hence exists k > 0 and n 0 > 1 such that x n ≥ k for n ≥ n 0. By summation of the fourth equation of system (S) we find that (9) leads to a contradiction with the positiveness of w n. □.
In Section 3, by employing the Guo-Krasnosel'skii fixed point theorem, we prove the existence of twin positive solutions for (1.1) under the positiveness of the Green function associated with (1.2 - 1.3 1.2 - 1.3
To the positiveness we apply some arguments of Chabrowski and Yang in [15] which we describe below.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com