Second-order Emden–Fowler neutral differential equations: A new precise criterion for oscillation
Osama Moaaz, Higinio Ramos, Jan Awrejcewicz
Abstract
This study aims at offering a new criterion for the oscillation of the solutions of Emden–Fowler second-order neutral differential equations. The approach used presents a non-traditional Riccati substitution and takes into account all the delay functions, which had been neglected in previous analyses. The new results essentially improve and simplify some well-known results reported in the literature. Furthermore, the new criterion provides precise results in the ordinary case (e.g. Euler-type equations), whereas the existing results fail in this case.
Topics & Concepts
MathematicsOscillation (cell signaling)Order (exchange)Euler's formulaApplied mathematicsOrdinary differential equationType (biology)Differential equationSubstitution (logic)Differential (mechanical device)Delay differential equationEuler equationsMathematical analysisComputer scienceProgramming languageFinanceBiologyEcologyAerospace engineeringGeneticsEconomicsEngineeringFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations