scholarly journals On variational formulations for functional differential equations

2007 ◽  
Vol 5 (1) ◽  
pp. 89-101 ◽  
Author(s):  
I. A. Kolesnikova ◽  
A. M. Popov ◽  
V. M. Savchin
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Variational Principles ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Partial Functional Differential Equations ◽  
Functional Differential ◽  
Necessary And Sufficient ◽  
Variational Formulations

Necessary and sufficient conditions for the existence of integral variational principles for boundary value problems for given ordinary and partial functional differential equations are obtained. Examples are given illustrating the results.

On nonlinear boundary value problems for higher order functional differential equations

2016 ◽  
Vol 23 (4) ◽  
pp. 537-550 ◽  
Author(s):  
Ivan Kiguradze ◽  
Zaza Sokhadze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Functional ◽  
Functional Differential

AbstractFor higher order nonlinear functional differential equations, sufficient conditions for the solvability and unique solvability of some nonlinear nonlocal boundary value problems are established.

scholarly journals Initial and boundary value problems for partial functional differential equations

1997 ◽  
Vol 10 (2) ◽  
pp. 157-168
Author(s):  
S. K. Ntouyas ◽  
P. Ch. Tsamatos
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Partial Functional Differential Equations ◽  
Point Analysis ◽  
Functional Differential

In this paper we study the existence of solutions to initial and boundary value problems of partial functional differential equations via a fixed-point analysis approach. Using the topological transversality theorem we derive conditions under which an initial or a boundary value problem has a solution.

Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations

2009 ◽  
Vol 16 (4) ◽  
pp. 617-628
Author(s):  
Guoping Chen ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Point Boundary ◽  
Functional Differential ◽  
Extreme Solutions

Abstract This paper is concerned with the existence of extreme solutions of nonlinear three-point boundary value problems for a class of first order impulsive functional differential equations. In the presence of a lower solution α and an upper solution β with the classical condition α ≤ β or the reversed ordering condition β ≤ α, some sufficient conditions for the existence of extreme solutions are obtained by using the method of upper and lower solutions coupled with the monotone iterative technique.

On Singular Boundary Value Problems for Functional Differential Equations of Higher Order

2001 ◽  
Vol 8 (4) ◽  
pp. 791-814
Author(s):  
I. Kiguradze ◽  
B. Půža ◽  
I. P. Stavroulakis
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Singular Boundary ◽  
Dimensional Vector ◽  
Singular Boundary Value Problems ◽  
Functional Differential

Abstract Sufficient conditions are established for the solvability of the boundary value problem 𝑥(𝑛) (𝑡) = 𝑓(𝑥)(𝑡), ℎ𝑖(𝑥) = 0 (𝑖 = 1, . . . , 𝑛), where 𝑓 is an operator (ℎ𝑖 (𝑖 = 1, . . . , 𝑛) are operators) acting from some subspace of the space of (𝑛 – 1)-times differentiable on the interval ]𝑎, 𝑏[ 𝑚-dimensional vector functions into the space of locally integrable on ]𝑎, 𝑏[ 𝑚-dimensional vector functions (into the space ).

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