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.