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.