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end{aligned} (5)We conclude via Lemmas 2.4 and 2.6.
Since 1≠0, we conclude (via disjunctive syllogism, which sanctions inferring sentence B from the sentences A ∨ B and ¬A) that DLiar is not true.
So there exists a constant C such that for all (y in B_{1/2}) there exist radii (r_j y) rightarrow 0) such that begin{aligned} Q_y u,r_j y))le C. end{aligned}We conclude via Lemma 2.6.
Hence, we conclude via the direct method of variational methods (see [20], Theorem 1.2) that there exists a global minimum point of I in (W_{0}) and, consequently, a solution of problem (1.2). □.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com