Abstract
The use of linking or sandwich pairs cannot produce critical points by themselves. The most they can produce are sequences satisfying
If such a sequence has a convergent subsequence, we obtain a critical point. Lacking such information, we cannot eliminate the possibility that
which destroys any hope of obtaining a critical point from this sequence. On the other hand, knowing that the sequence is bounded does not guarantee a critical point either. But there is a difference. In many applications, knowing that a sequence satisfying (4.1) is bounded allows one to obtain a convergent subsequence. This is just what is needed. For such applications it would be very helpful if we could obtain a bounded sequence satisfying (4.1). This leads to the question: Is there anything we can do to obtain such a sequence?
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Schechter, M. (2020). The Monotonicity Trick. In: Critical Point Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-45603-0_4
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