Abstract: This paper
is devoted to the study of the bifurcation problem for monotone type operators,
extending the well-known local and global bifurcation results via the Berkovits
degree theory. We show that under certain monotonicity conditions, the local and
global Kranoselskii and Rabinovitz bifurcation results for mapping of the from
can be
extended to mapping of the type
In the first part, we
introduce the definition of monotone type mappings and concepts needed for our
study. The second part is devoted to the study of the local bifurcation result.
The third part deals with the extension of the global bifurcation result to
operators of monotone type.
Keywords and phrases: local bifurcation, global bifurcation, monotone operators, Kranoselskii, Rabinovitz, degree theory.
