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The first motivation for this note is to obtain a general version
of the following result: let E be a Banach space and f : E → R be a differentiable
function, bounded below and satisfying the Palais-Smale condition; then, f is coercive,
i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and
extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references
therein.
A general result of this type was given in [3, Theorem 5.1] for a lower...
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