Three positive periodic solutions of second order nonlinear neutral functional differential equations with delayed derivative

Autor:	He Yang, Lu Zhang
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Neutral functional differential equation Positive periodic solution Delayed derivative Cone Leggett–Williams fixed point theorem Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-12 (2020)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-020-02630-z
Popis:	Abstract This paper deals with the existence of three positive periodic solutions for a class of second order neutral functional differential equations involving the delayed derivative term in nonlinearity ( x ( t ) − c x ( t − δ ) ) ″ + a ( t ) g ( x ( t ) ) x ( t ) = λ b ( t ) f ( t , x ( t ) , x ( t − τ 1 ( t ) ) , x ′ ( t − τ 2 ( t ) ) ) $(x(t)-cx(t-\delta)){''}+a(t)g(x(t))x(t)=\lambda b(t)f(t,x(t),x(t-\tau_{1}(t)),x'(t-\tau_{2}(t)))$ . By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established.
Databáze:	Directory of Open Access Journals
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