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arXiv · 1406.1026

Singular points of non-monotone potential operators

Biagio Ricceri
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Abstract

In this paper, we establish some results about the singular points of certain non-monotone potential operators. Here is a sample: If $X$ is an infinite-dimensional reflexive real Banach space and if $T:X\to X^*$ is a non-monotone, closed, continuous potential operator such that the functional $x\to \int_0^1T(sx)(x)ds$ is sequentially weakly lower semicontinuous and $\lim_{\|x\|\to +\infty}(\int_0^1T(sx)(x)ds+φ(x))=+\infty$ for all $φ\in X^*$, then the set of all singular points of $T$ is not $σ$-compact.

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Biagio Ricceri. 2014-09-12. Singular points of non-monotone potential operators. https://arxiv.org/abs/1406.1026

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