The research group in Mathematical Analysis at the University of Sassari aims to study new theories, new methodologies, and new theorems in the field of mathematical analysis. The main active research areas are: Linear and nonlinear analysis; Existence, non-existence, and multiplicity of solutions to elliptic partial differential equations or systems of equations; Qualitative properties of solutions to elliptic partial differential equations or systems of equations; Bifurcation problems and symmetry breaking for solutions to partial differential equations; Reaction-diffusion equations; Mathematical models in life sciences; Singularly perturbed problems; Self-adjoint and non-self-adjoint spectral theory, with applications to quantum mechanics, electromagnetism, fluid dynamics, and linear elasticity theory; Stability and instability of solutions to partial differential equations as the geometry of the domain varies; Unitary representations of the free group and other similar discrete groups; Study of complex systems.

Hebisch W., Kuhn G., Steger T. (2022). FREE GROUP REPRESENTATIONS: DUPLICITY AND ODDITY ON THE BOUNDARY. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 375, p. 1825-1860, ISSN: 1088-6850, doi: 10.1090/tran/8546

 -Spectral analysis and domain truncation for Maxwell's equations Bögli, S., Ferraresso, F., Marletta, M., Tretter, C. Journal des Mathematiques Pures et Appliquees, 2023, 170, pp. 96–135

 -Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation Ferraresso, F., Marletta, M. Journal of Differential Equations, 2023, 346, pp. 313–346

 -On the number of critical points of solutions of semilinear equations in R^2, Gladiali, F., Grossi, M. American Journal of Mathematics, 2022, 144(5), pp. 1221–1240

 -Nonradial solutions for the Hénon equation in R^N, Gladiali, F., Grossi, M., Neves, S.L.N. Advances in Mathematics, 2013, 249, pp. 1–36

Qualitative study of dynamical systems

Mathematical modeling of biochemical phenomena