scholarly journals Existence of solutions for a class of abstract neutral differential equations

2017 ◽  
Vol 37 (5) ◽  
pp. 2455-2482 ◽  
Author(s):  
Hernán R. Henríquez ◽  
◽  
Claudio Cuevas ◽  
Juan C. Pozo ◽  
Herme Soto ◽  
...  
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Neutral Differential Equations

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

2012 ◽  
Vol 55 (4) ◽  
pp. 736-751 ◽  
Author(s):  
Eduardo Hernández ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Classical Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

AbstractIn this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

scholarly journals The Existence of Solutions for Impulsive Fractional Partial Neutral Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Fei Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Neutral Differential Equations ◽  
Analytical Results ◽  
Fixed Point Methods

This paper deals with the existence of mild solutions of a class of impulsive fractional partial neutral semilinear differential equations. A series of analytical results about the mild solutions are obtained by using fixed-point methods. Then, we present an example to further illustrate the applications of these results.

scholarly journals Existence of solutions to Sobolev-type partial neutral differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Shruti Agarwal ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Neutral Differential Equation ◽  
Sobolev Type ◽  
Neutral Differential Equations

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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