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 ← X* is a non-monotone, closed, continuous potential operator such that the functional x ∫10 T(sx)(x)ds is sequentially weakly lower semicontinuous and lim∥x∥←+∞(∫01 T(sx)(x)ds + ϕ(x)) = +∞for all ϕε X*, then the set of all singular points of T is not sigma;-compact.

Singular points of non-monotone potential operators

RICCERI, Biagio
2015

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 ← X* is a non-monotone, closed, continuous potential operator such that the functional x ∫10 T(sx)(x)ds is sequentially weakly lower semicontinuous and lim∥x∥←+∞(∫01 T(sx)(x)ds + ϕ(x)) = +∞for all ϕε X*, then the set of all singular points of T is not sigma;-compact.
Fredholm operator, Minimax theorem, Non-monotone operator, Potential operator, Singular point.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/16772
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