The research team studies nonlinear differential and difference equations, which serve as mathematical models for a wide range of natural and technical processes. The focus is primarily on the qualitative and quantitative analysis of nonlinear ordinary and partial differential equations, i.e., questions of existence, uniqueness, or multiplicity and bifurcations of solutions, which are crucial for understanding the behaviour of the modelled systems and the setting of their parameters. The research team also investigates stochastic equations and nonlinear continuous and discrete systems, including problems on time scales or graph structures.
Specific topics of interest include, in particular, fluid flow in porous media, vibrations of asymmetric structures, dynamics in biomaterials, living organisms and populations at both microscopic and macroscopic levels, and the dynamics of social processes.