Oscillation of higher order delay differential equations
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A sufficient condition was obtained for oscillation of all solutions of theodd-order delay differential equation$$x^{(n)} (t) + \sum\limits_{i = 1}^m {p_i (t)} x(t - \sigma _{_i } ) = 0,$$ wherep_{i}(t) are non-negative real valued continuous function in [T ∞] for someT≥0 and σ_{i},∈(0, ∞)(i = 1,2,…,m). In particular, forp_{i}(t) =p_{i}∈(0, ∞) andn > 1 the result reduces to$$\frac{1}{m}\left( {\sum\limits_{i = 1}^m {(p_i \sigma _i^m )^{1/2} } } \right)^2 > (n - 2)!\frac{{(n)^n }}{e},$$ implies that every solution of (*) oscillates. This result supplements forn > 1 to a similar result proved by Ladaset al [J. Diff. Equn.,42 (1982) 134–152] which was proved for the casen = 1.
P Das^{1} N Misra^{1} ^{2} B B Mishra^{1}
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November 2019
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