scholarly journals Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Yongzeng Lai ◽  
Fei Xu
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Lower Semicontinuous ◽  
Functional Differential Equations ◽  
Conjugate Function ◽  
Point Theory ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Nonlinear Functional ◽  
Functional Differential

By introducing subdifferentiability of lower semicontinuous convex functionφ(x(t),x(t−τ))and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equationx″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0,x(0)=0.

scholarly journals Existence of Periodic Solutions to Multidelay Functional Differential Equations of Second Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Ramazan Yazgan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Functional Approach ◽  
Second Order ◽  
Nonlinear Functional ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

Using Lyapunov-Krasovskii functional approach, we establish a new result to guarantee the existence of periodic solutions of a certain multidelay nonlinear functional differential equation of second order. By this work, we extend and improve some earlier result in the literature.

scholarly journals Multiple Periodic Solutions for a Class of Second-Order Neutral Impulsive Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Jingli Xie ◽  
Zhiguo Luo ◽  
Yuhua Zeng
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Second Order ◽  
Multiple Periodic Solutions ◽  
Functional Differential

In this paper, we study a class of second-order neutral impulsive functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of critical point theory and variational methods. We propose an example to illustrate the applicability of our result.

scholarly journals Study of periodic and nonnegative periodic solutions of nonlinear neutral functional differential equations via fixed points

2016 ◽  
Vol 8 (2) ◽  
pp. 255-270
Author(s):  
Mouataz Billah Mesmouli ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Neutral Functional Differential Equations ◽  
Completely Continuous ◽  
Continuous Map ◽  
Functional Differential ◽  
Large Contraction

Abstract In this paper, we study the existence of periodic and non-negative periodic solutions of the nonlinear neutral differential equation $${{\rm{d}} \over {{\rm{dt}}}}{\rm{x}}({\rm{t}}) = - {\rm{a}}\;({\rm{t}})\;{\rm{h}}\;({\rm{x}}\;({\rm{t}})) + {{\rm{d}} \over {{\rm{dt}}}}{\rm{Q}}\;({\rm{t}},\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))) + {\rm{G}}\;({\rm{t}},\;{\rm{x}}({\rm{t}}),\;{\rm{x}}\;({\rm{t}} - {\rm \tau} \;({\rm{t}}))).$$ We invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modificatition of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions Q and G.

scholarly journals Strong oscillations for second order nonlinear functional differential equations

1990 ◽  
Vol 13 (1) ◽  
pp. 151-158
Author(s):  
Jurang Yan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Second Order ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Oscillation Theorems

In this paper, we establish some strongly oscillation theorems for nonlinear second order functional differential equationx″(t)+p(t)f(x(t),x(g(t)))=0without assuming thatg(t)is retarded or advanced.

scholarly journals Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Shurong Sun ◽  
Tongxing Li ◽  
Zhenlai Han ◽  
Yibing Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Mixed Nonlinearities ◽  
Functional Differential

We study the following second-order neutral functional differential equation with mixed nonlinearities(r(t)|(u(t)+p(t)u(t-σ))'|α-1(u(t)+p(t)u(t-σ))′)′+q0(t)|u(τ0(t))|α-1u(τ0(t))+q1(t)|u(τ1(t))|β-1u(τ1(t))+q2(t)|u(τ2(t))|γ-1u(τ2(t))=0, whereγ>α>β>0,∫t0∞(1/r1/α(t))dt<∞. Oscillation results for the equation are established which improve the results obtained by Sun and Meng (2006), Xu and Meng (2006), Sun and Meng (2009), and Han et al. (2010).

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