Necessary and Sufficient Conditions for Oscillations to a Second-Order Neutral Differential Equations with Impulses
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Authors: A. K. TRIPATHY AND S. S. SANTRA
DOI: 10.46793/KgJMat2301.081T
Abstract:
In this work, we obtain necessary and sufficient conditions for oscillation of solutions of second-order neutral impulsive differential system
 |
where z(t) = x(t) + p(t)x(τ(t)). Under the assumption
∫
0∞
r(η)
−1∕γdη = ∞, we consider two cases when γ > αi and
γ < αi. Our main tool is Lebesgue’s Dominated Convergence theorem.
Examples are given to illustrate our main results and we state an open
problem.
Keywords:
Oscillation, non-oscillation, neutral, delay, Lebesgue’s dominated convergence theorem, impulses.
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