Two new proofs for the boundedness of solutions to \(x^{\prime\prime}+a(t)x = 0\). (English) Zbl 1271.34038

Summary: Two theorems are presented concerning the well-known linear differential equation \(x^{\prime\prime}+a(t)x=0\). While the results are not new, the proofs presented simplify previous work since the Gronwall inequality is avoided which is the usual case.


34C11 Growth and boundedness of solutions to ordinary differential equations
Full Text: Euclid


[1] D. Sanchez, Ordinary Differential Equations and Stability Theory: An Introduction , Dover, New York, 1979. · Zbl 0465.34001
[2] C. Tunç, A note on boundedness of solutions to a class or non-autonomous differential equations of second order, Appl. Anal. Discrete Math. , 18 (2010), 361-372. · Zbl 1299.34128
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