Sublevel sets and global minima of coercive functionals and local minima of their perturbations

By Biagio Ricceri. 2004

51 citations recorded by the source corpus.

The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following conclusion holds: if, for some $r > \inf_X \Psi$, the weak closure of the set $\Psi^{-1}(]-\infty, r[)$ has at least $k$ connected components in the weak topology, then, for each $\lambda > 0$ small enough, the functional $\Psi + \lambda\Phi$ has at least $k$ local minima lying in $\Psi^{-1}(]-\infty, r[)$.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/72b4b029231d215f2c9ac9198ba78e846bf0719d

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities (2009, background): “Faraci [12] produces two or three solutions for certain parametric problems, when the parameter is small, employing a further abstract multiplicity result of Ricceri [26].”