Challenges to global solutions in Horndeski's theory

We explore the question of obtaining global solutions in Horndeski's theories of gravity. Toward this end, we study a relevant set of the theory and, by employing the Einstein frame we simplify the analysis by exploiting known results on global solutions of wave equations. We identify conditions for achieving global solutions as well as obstacles that can arise to spoil such goal. We illustrate such problems via numerical simulations.