I
am interested in the study of some nonlinear elliptic
equations regarding existence of solutions and its
qualitative properties. The elliptic operator involved
in the problems to study may be: linear, like the
Laplacian; quasilinear, such as the m-Laplacian; or
fully nonlinear, such as the Pucci's extremal
operators. Principally, I am working in three lines of
research: first, a line associated to problems with
boundary blow-up, second, other one associated to
concentration phenomena, and a third line associated
to problems of Liouville-type. Recently, I am also
studying blow-up of solutions for some parabolic
boundary problems and some problems involving the
fractional operator.