Variational Methods for Strongly Indefinite Problems

Abstract

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“…Thus the space L 2 possesses the orthogonal decomposition: [10,14]) be equipped with the inner product…”

Multiple periodic solutions to a class of nonautonomous second-order delay differential equation

“…is complete. Author details 1 School of Mathematical Science, Shanxi University, Wucheng Road, Taiyuan, 030006, P.R. China.…”

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“…First, by Lemma 3.1, a standard argument shows that {z j } is bounded (see, e.g., [18]). Next, by the conclusion (iii) of Lemma 3.1, it holds that…”

“…Note that, by (H 0 )-(H 4 ), it is not difficult to show that S min is bounded in E (cf. [16] or [18]), hence, |u| 2 ≤ C 2 for all u ∈ S min and some C 2 . Therefore, as a consequence of Lemma 2.8 we see that, for each q ∈ [2, ∞), there is Λ q > 0 such that…”