Existence of Solutions for Second Order Partial Neutral Functional Differential Equations

2008 ◽  
Vol 62 (2) ◽  
pp. 191-217 ◽  
Author(s):  
Eduardo Hernández Morales ◽  
Hernán R. Henríquez ◽  
Mark A. McKibben
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

scholarly journals EXISTENCE OF SOLUTIONS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

1999 ◽  
Vol 30 (4) ◽  
pp. 299-309
Author(s):  
K. BALACHANDRAN ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Cosine Families ◽  
Functional Differential

Sufficient conditions for existence of mild solutions for second order neutral functional differential equations are established by using the theory of strongly continuous cosine families and the Schaefer theorem.

scholarly journals Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shurong Sun ◽  
Tongxing Li ◽  
Zhenlai Han ◽  
Hua Li
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Oscillation Criteria ◽  
Functional Differential ◽  
Oscillation Theorems

New oscillation criteria are established for the second-order nonlinear neutral functional differential equations of the form(r(t)|z′(t)|α−1z′(t))’+f(t,x[σ(t)])=0,t≥t0, wherez(t)=x(t)+p(t)x(τ(t)),p∈C1([t0,∞),[0,∞)), andα≥1. Our results improve and extend some known results in the literature. Some examples are also provided to show the importance of these results.

scholarly journals Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Meili Li ◽  
Chunhai Kou
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Power Of Operators

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem.

scholarly journals Oscillation theorems of solution of second-order neutral differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12771-12779
Author(s):  
Ali Muhib ◽  
◽  
Hammad Alotaibi ◽  
Omar Bazighifan ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Theoretical Support ◽  
Functional Differential ◽  
Oscillation Theorems ◽  
New Criteria ◽  
Oscillation Of Solutions

<abstract><p>In this paper, we aim to explore the oscillation of solutions for a class of second-order neutral functional differential equations. We propose new criteria to ensure that all obtained solutions are oscillatory. The obtained results can be used to develop and provide theoretical support for and further develop the oscillation study for a class of second-order neutral differential equations. Finally, an illustrated example is given to demonstrate the effectiveness of our new criteria.</p></abstract>

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