The order topology has been historically defined only for totally ordered sets. Here, the order topology in partially ordered sets will be constructed. Several attempts have been provided in the recent litera-ture on partially ordered groups, rings and modules. This manuscript contains a full construction that provides solid foundational ground to the previous attempts and serves to pay tribute to the topological trajectory of Prof. Ricceri.

In this paper, we extend two topological minimax theorems due to Ricceri to the case of two functions.

In this note we investigate the regularity theory for weak solutions of second-order elliptic partial differential equations whose coefficients belong to the space of functions of bounded mean oscillation (BMO). The main contribution of this work is to establish that weak solutions possess second derivatives in appropriate Lq spaces. Our techniques combine harmonic analysis, variational methods, and delicate pertur-bation estimates.

The existence and location of solutions are established for an elliptic system with full gradient dependence and intrinsic operators. The abstract results are applied to a system with convolution products.

We introduce a new class of generalized metric spaces with graphs and prove a fixed point result for Rakotch type contractive mappings.

We study an elliptic equation, with homogeneous Dirichlet bound-ary conditions, driven by a mixed type operator (the sum of the Lapla-cian and the fractional Laplacian), involving a parametric reaction and an undetermined source term. Applying a recent abstract critical point theorem of Ricceri, we prove existence of a solution for a convenient source and small enough parameters.

Biagio Ricceri was born in Catania, on February 7, 1955. After graduating in Mathematics from the University of Catania, he was a fellow of the italian National Research Council from 1979 to 1982. In 1983, he became assistant professor at the University of Catania and, in 1987, he was appointed full professor at the University of Messina. In 1997, he returned to the University of Catania. He retired on November 1, 2025. Without going into much detail, I can say that Professor Biagio Ricceri was an excellent educator of several generations of students and the scientific mentor of 13 PhD students who are currently full or associate professors. …

In this paper, we study existence and main properties of weak so-lutions for a class of boundary value problems.

We establish a generalization of Ekeland’s variational principle for submonotone maps defined on a preordered pseudometric space and with values in a preordered monoid. The proof relies on an ordering principle for more general preordered sets.

We investigate weak solutions of a quasilinear (p, p)-biharmonic sys-tem with variational structure. Using the principal eigenvalue of the associated system and the linking theorem of Brezis and Nirenberg, we establish the existence of at least two nontrivial weak solutions for the eigenvalue parameter λ in a closed right neighborhood of zero. Our results apply in both resonant and nonresonant cases, depending on the asymptotic behavior of the nonlinear term. These findings extend earlier work on scalar biharmonic equations and systems, and cover several important special cases arising from different choices of the coefficients.