Oscillation of higher order delay differential equations |
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Authors: | P Das N Misra B B Mishra |
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Institution: | 1. Department of Mathematics, Indira Gandhi Institute of Technology, Sarang, Talcher, Orissa, India 2. Department of Mathematics, Berhampur University, 760007, Berhampur, India
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Abstract: | 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 σi,∈(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. |
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