Necessary and sufficient conditions for oscillation of second-order differential equation with several delays
DOI:
https://doi.org/10.24193/subbmath.2023.2.08Keywords:
Oscillation, nonoscillation, nonlinear, delay argument, second-order differential equation, Lebesgue’s dominated convergence theorem.Abstract
In this paper, necessary and sufficient conditions are establish of the solutions to second-order delay differential equations of the form
We consider two cases when fi(u)/uβ is non-increasing for β < γ, and non- decreasing for β > γ where β and γ are the quotient of two positive odd integers. Our main tool is Lebesgue’s Dominated Convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.
Mathematics Subject Classification (2010): 34C10, 34C15, 34K11.
Received 18 April 2020; Accepted 10 May 2020.
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