Modelling of phenomena in applied sciences like physics, biology or engineering  often leads to equations depending on parameters. These parameters describe how the environment influences a system. Thus, the knowledge of the values of the parameters at which the qualitative behaviour of the system changes has great importance. In this talk we study the structure of  equations of the form $F(x,\lambda)=0,$ where $F$ is a nonlinear operator between Banach spaces and $\lambda$ represents the parameters.