Título:  On a Critical Point Theorem for Nondifferentiable Functionals

Palestrante:  Ricardo Lima Alves (UFAC)

Abstract.: We revisit Weierstrass’s theorem for functionals I : A → R, where A is
a compact topological space. Then, motivated by Alves-Santos-Silva [1], we provide a
result for nondifferentiable functionals that ensures the existence of global minimizers
and that these are also solutions of a functional equation. An application to a nonsmooth
integro-differential problem is presented.

References
[1] Alves, R.L., Santos, C.A., Silva, K. Extremal Regions and Multiplicity of Positive
Solutions for Singular Superlinear Elliptic Systems with Indefinite-Sign Potential.
Milan J. Math. 91, 213–253 (2023). https://doi.org/10.1007/s00032-023-00379-0
[2] Lima Alves, R. Existence of Positive Solution for a Singular Elliptic Problem
with an Asymptotically Linear Nonlinearity. Mediterr. J. Math. 18, 4 (2021).
https://doi.org/10.1007/s00009-020-01646-9
[3] Santos, G.C.G.d., Lima, N.d.A. and Lima, R.N.d. Existence of solution for a class
of integro–differential sublinear problems with strong singularity. Z. Angew. Math.
Phys. 74, 196 (2023). https://doi.org/10.1007/s00033-023-02085-8