Necessary and Sufficient Conditions for Oscillations to a Second-Order Neutral Differential Equations with Impulses
ARUN KUMAR TRIPATHY, Shyam Sundar Santra
Abstract
In this work, we obtain necessary and sufficient conditions for oscillation of solutions of second-order neutral impulsive differential systemwhere z(t) = x(t) + p(t)x(τ (t)).Under the assumptionwe consider two cases when γ > α i and γ < α i .Our main tool is Lebesgue's Dominated Convergence theorem.Examples are given to illustrate our main results and we state an open problem.
Topics & Concepts
MathematicsOscillation (cell signaling)Lebesgue integrationOrder (exchange)Convergence (economics)Differential equationComparison theoremState (computer science)Mathematical analysisDifferential (mechanical device)Work (physics)Applied mathematicsPure mathematicsPhysicsThermodynamicsAlgorithmFinanceBiologyEconomicsEconomic growthGeneticsNonlinear Differential Equations AnalysisDifferential Equations and Numerical MethodsDifferential Equations and Boundary Problems