The study of functions and their properties is the focus of some areas of mathematics, such
as Analysis, Differential Equations and Applied Mathematics. The objective of this work is
to present a set of Ambrosetti-Prod type results, which consists of solving a (P) equation of
the form G(u, s) = 0, finding a real parameter s and a value s1 ∈ R, where the equation (P)
is no longer a solution when s < s1, has at least one solution when s = s1 e have at least
two when s > s1. We present a study of three equations, a simple one, and the other two
differential equations, namely: f(u) = s, u 0 (x) + f(u(x)) = s e u 0 (x) + f(x, u(x)) = s.
This work was based on the first chapters of the article [1], it has a qualitative approach and
the research is a bibliographical one, since it tried to understand the behavior of the solutions
of an equation without worrying about finding them.
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