Norm estimates for fundamental solutions of neutral type functional differential equations

2012 ◽  
Vol 4 (3) ◽  
pp. 255 ◽  
Author(s):  
Michael Gil'
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Fundamental Solutions ◽  
Norm Estimates ◽  
Functional Differential

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

scholarly journals On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1418
Author(s):  
Clement McCalla
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Fundamental Solutions ◽  
Exact Expression ◽  
System Structure ◽  
Characteristic Matrix ◽  
Kernel Matrix ◽  
Resolvent Matrix ◽  
Functional Differential

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix; and the Laplace transform. The fundamental solution is presented in the form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of an RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

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