The Necessary and sufficient conditions for the oscillation of solutions to a second-order neutral differential equation with impulses
Shyam Sundar Santra, Julio G. Dix
2020Nonlinear studies11 citations
Abstract
In this work, we obtain necessary and sufficient conditions for the oscillation of the solutions to a second-order neutral differential equation with impulses. Our main tool is Lebesgue's Dominated Convergence Theorem. We illustrate our results with two examples and state an open problem.
Topics & Concepts
Oscillation (cell signaling)Lebesgue integrationConvergence (economics)Differential equationMathematicsOrder (exchange)Mathematical analysisFunctional differential equationDifferential (mechanical device)Work (physics)Applied mathematicsPhysicsQuantum mechanicsEconomicsThermodynamicsFinanceBiologyEconomic growthGeneticsNonlinear Differential Equations AnalysisDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods