Necessary and Sufficient Condition for Oscillatory and Asymptotic Behaviour of Second-Order Functional Differential Equations
Shyam Sundar Santra
Abstract
In this paper, necessary and sufficient conditions are obtained for oscillatory and asymptotic behaviour of solutions of second-order neutral delay differential equations of the formunder the assumption ∞ 1 r(η) dη = ∞ for various ranges of the bounded neutral coefficient p.Our main tools are Lebesgue's dominated convergence theorem and Banach's contraction mapping principle.Further, an illustrative example showing the applicability of the new results is included.
Topics & Concepts
MathematicsLebesgue integrationBounded functionOrder (exchange)Contraction principleBanach spaceMathematical analysisDifferential equationConvergence (economics)Applied mathematicsUniquenessEconomic growthEconomicsFinanceNonlinear Differential Equations AnalysisDifferential Equations and Numerical MethodsDifferential Equations and Boundary Problems