The research activity employs variational techniques and methods from nonlinear analysis to address problems of existence, multiplicity, and qualitative properties of entire solutions (on ℝⁿ) to semilinear elliptic equations and systems arising in mathematical physics, such as Ginzburg–Landau, Allen–Cahn, Sine–Gordon, and the stationary Schrödinger equation. The approach is based on an energy-functional formulation and on the search for critical points via constrained minimization and minimax methods, combined with concentration–compactness techniques to deal with loss of compactness in unbounded domains. A central goal is to prove the existence and multiplicity of solutions under symmetry constraints, including periodic brake-orbit solutions, as well as multibump solutions and other families with prescribed special symmetries. Nondegeneracy conditions are also investigated, as they are instrumental in establishing the presence of complex (possibly chaotic) dynamics in the systems under consideration.
Prof.ssa Francesca Gemma Alessio
Tel. +39 071 220 4477
email: f.g.alessio@univpm.it
