• B B Mishra

Articles written in Proceedings – Mathematical Sciences

• Oscillation of higher order delay differential equations

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019