Singular points of non-monotone potential operators

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 $T:X\to X^{\ast }$ is a non-monotone, closed, continuous potential operator such that the functional $x\to {\int }_0^{1}T(sx)(x)ds$ is sequentially weakly lower semicontinuous and ${\lim }_{\Vert x\Vert \to +\infty }({\int }_0^{1}T(sx)(x)ds+\phi (x))=+\infty$ for all $\phi \in X^{\ast }$, then the set of all singular points of $T$ is not $\sigma$-compact.

References in corpus (2)

• A further improvement of a minimax theorem of Borenshtein and Shulman
• Weights sharing the same eigenvalue

Cited by in corpus (1)

• Weights sharing the same eigenvalue