On a periodic boundary value problem for cyclic feedback type linear functional differential systems

2006 ◽  
Vol 87 (3) ◽  
pp. 255-260 ◽  
Author(s):  
Sulkhan Mukhigulashvili
Keyword(s):  
Boundary Value Problem ◽  
Linear Functional ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Differential Systems ◽  
Feedback Type ◽  
Functional Differential Systems ◽  
Functional Differential

On a Boundary Value Problem for 𝑛-th Order Linear Functional Differential Systems

2005 ◽  
Vol 12 (2) ◽  
pp. 229-236
Author(s):  
Robert Hakl ◽  
Sulkhan Mukhigulashvili
Keyword(s):  
Boundary Value Problem ◽  
Linear Functional ◽  
Boundary Value ◽  
Fredholm Alternative ◽  
Linear Boundary ◽  
Bounded Operators ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Linear Boundary Value Problem

Abstract In this paper, theorems on the Fredholm alternative and wellposedness of the linear boundary value problem 𝑢′(𝑡) = ℓ(𝑢)(𝑡) + 𝑞(𝑡), ℎ(𝑢) = 𝑐, where ℓ : 𝐶([𝑎, 𝑏]; 𝑅𝑛) → 𝐿([𝑎, 𝑏]; 𝑅𝑛) and ℎ : 𝐶([𝑎, 𝑏]; 𝑅𝑛) → 𝑅𝑛 are linear bounded operators, 𝑞 ∈ 𝐿([𝑎, 𝑏]; 𝑅𝑛), and 𝑐 ∈ 𝑅𝑛, are established even when ℓ is not a strongly bounded operator.

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