scholarly journals Study of Solutions to Some Functional Differential Equations with Piecewise Constant Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Juan J. Nieto ◽  
Rosana Rodríguez-López
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
The State ◽  
State Function ◽  
Uniqueness Of Solutions ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Functional Differential

We provide optimal conditions for the existence and uniqueness of solutions to a nonlocal boundary value problem for a class of linear homogeneous second-order functional differential equations with piecewise constant arguments. The nonlocal boundary conditions include terms of the state function and the derivative of the state function. A similar nonhomogeneous problem is also discussed.

scholarly journals Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 4
Author(s):  
Gennaro Infante
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Short Note ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Growth Conditions ◽  
Functional Differential Systems ◽  
Functional Differential

Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations subject to functional boundary conditions. We obtain a localization of the corresponding non-negative eigenfunctions in terms of their norm. Under additional growth conditions, we also prove the existence of an unbounded set of eigenfunctions for these systems. The class of equations that we study is fairly general and our approach covers some systems of nonlocal elliptic differential equations subject to nonlocal boundary conditions. An example is presented to illustrate the theory.

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.

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

2010 ◽  
Vol 60 (3) ◽  
Author(s):  
N. Dilna ◽  
A. Ronto
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Unique Solvability ◽  
Linear Functional ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Local Boundary ◽  
Non Linear ◽  
Functional Differential

AbstractGeneral conditions for the unique solvability of a non-linear nonlocal boundary-value problem for systems of non-linear functional differential equations are obtained.

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