You have 3 types when lambda = 0 lamda < 0 and lambda > 0
But how do you know which cases to use??
It might help if you told us what in the world you are talking about! What is lambda?
It looks like you are talking about determining whether a partial differential equation is "hyperbolic", "parabolic", or "elliptic" but without further information on the given form of the equation, about the best I can say is to look up the definition of each of those.