Research topics

Several different areas are currently subject of research.

  • Study of the period function of plane centers, in relation to the existence and/or uniqueness of critical orbits, convexity, monotonicity partitions.
  • Existence, uniqueness, multiplicity of limit cycles of planar systems.
  • Global invertibility of locally invertible maps.
  • Application of the dynamic programming method and study of the corresponding Bellman/Isaacs equation in the viscosity sense, concerning with
    • optimal control problems and differential games with hybrid thermostatically switching dynamics;
    • optimal control of more general ordinary differential systems with hysteresis effects, and applications.
  • Mean field games and applications.
  • Null controllability of semilinear parabolic equations with hysteresis.
  • Mathematical models applied to biology, ecology, and epidemiology. Bifurcation analysis.