Stable non-singular solutions in beyond Horndeski theories

The theory of interest is Generalized Galileon or Horndeski theory
(and beyond). We start with motivation to study these theories. Then
we discuss the stability issue in two different types of scenarios:
cosmological and static, spherically-symmetric case. We show, that it
leads to the no-go theorems for non-singular solutions in Horndeski
theory. Finally we show the possibility to obtain stable solutions in
beyond Horndeski theory and discuss further issues.