In the note, two theorems are presented concerning the well-known linear differential equation $x''+a(t)x=0$. While the results are not new, the proofs presented simplify previous work since the Gronwall inequality is avoided which is the usual case.
Allan J. Kroopnick. "Two New Proofs for the Boundedness of Solutions to $x'' + a(t) x = 0$." Missouri J. Math. Sci. 25 (1) 103 - 105, May 2013. https://doi.org/10.35834/mjms/1369746402