Analyticity with respect to a parameter of a solution of a general linear boundary-value problem for a functional-differential equation

1995 ◽  
Vol 74 (5) ◽  
pp. 1280-1282
Author(s):  
R. F. Sagitov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Boundary Value ◽  
General Linear ◽  
Linear Boundary ◽  
Functional Differential ◽  
Linear Boundary Value Problem

scholarly journals On a boundary value problem for scalar linear functional differential equations

2004 ◽  
Vol 2004 (1) ◽  
pp. 45-67 ◽  
Author(s):  
R. Hakl ◽  
A. Lomtatidze ◽  
I. P. Stavroulakis
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Homogeneous Equation ◽  
Functional Differential Equations ◽  
Solution Space ◽  
Fredholm Alternative ◽  
Linear Boundary ◽  
Bounded Operators ◽  
Functional Differential ◽  
Linear Boundary Value Problem

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problemu′(t)=ℓ(u)(t)+q(t),h(u)=c, whereℓ:C([a,b];ℝ)→L([a,b];ℝ)andh:C([a,b];ℝ)→ℝare linear bounded operators,q∈L([a,b];ℝ), andc∈ℝ, are established even in the case whenℓis not astrongly boundedoperator. The question on the dimension of the solution space of the homogeneous equationu′(t)=ℓ(u)(t)is discussed as well.

On the solvability of a linear boundary value problem for a class of neutral type functional differential equations

1982 ◽  
Vol 93 (1-2) ◽  
pp. 25-31
Author(s):  
N. G. Kazakova ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Linear Boundary ◽  
Necessary And Sufficient Condition ◽  
Functional Differential ◽  
Necessary And Sufficient ◽  
Linear Boundary Value Problem

SynopsisThe paper considers a linear non-homogeneous boundary value problem for a class of neutral type functional differential equations. A necessary and sufficient condition for the existence of a unique solution of that problem is obtained.

On the spectral properties and positivity of solutionsof a periodic boundary value problemfor a second-order functional differential equation

2020 ◽  
pp. 123-130
Author(s):  
Manuel J. Alves ◽  
Sergey M. Labovskiy
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Spectral Properties ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Functional Differential ◽  
The Green Function

For a functional-differential operator Lu = (1/ρ)(-(pu')' + ∫_0^l▒〖u(s)d_s r(x,s)〗) with symmetry, the completeness and orthogonality of the eigenfunctions is shown. Thepositivity conditions of the Green function of the periodic boundary value problem areobtained.

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