
The paper deals with oscillatory properties of the forced third order equation (E) \(y''+ a(t) y'+ b(t) y'+ c(t) y= f(t)\) under the assumption that the functions \(a\), \(b\), \(c\), \(f\) are sufficiently smooth and \(b- a'\), \(-c\) and \(f\) are nonincreasing for large \(t\). It is shown that \((E)\) admits an oscillatory solution provided \[ \int^\infty \Biggl[ {{2a^2 (t)} \over {27}} - {{a(t) b(t)- a'(t))} \over 3} + c(t) - {2\over {3\sqrt {3}}} \biggl( {{a^2 (t)} \over 3} - (b(t)- a' (t)) \biggr)^{3/2} \Biggr] dt= \infty. \] This statement extends the known result that equation (E), where \(a, c, f>0\), \(b0. \]
forced third order equation, Applied Mathematics, Linear ordinary differential equations and systems, oscillatory properties, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Analysis
forced third order equation, Applied Mathematics, Linear ordinary differential equations and systems, oscillatory properties, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Analysis
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