scholarly journals Errata to ‘‘Some new analytical techniques and their application to irregular cases for the third order ordinary linear boundary-value problem”

1962 ◽  
Vol 103 (3) ◽  
pp. 559
Author(s):  
Nathaniel R. Stanley
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Analytical Techniques ◽  
Linear Boundary ◽  
Third Order ◽  
The Third ◽  
Linear Boundary Value Problem

scholarly journals Existence and uniqueness theorems for a third-order generalized boundary value problem

1989 ◽  
Vol 2 (1) ◽  
pp. 33-51
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Linear Boundary ◽  
Third Order ◽  
The Third ◽  
Special Cases ◽  
Linear Boundary Value Problem ◽  
Natural Way

Let f:[0,1]×ℝ3→ℝ be a function satisfying Caratheodory's conditions, e(x)∈L1[0,1], η∈[0,1], h≥0, k≥0, h+k>0. This paper studies existence and uniqueness questions for the third-order three-point generalized boundary value problem u‴+f(x,u,u′,u″)=e(x),   0<x<1, u(η)=0,   u″(0)−hu′(0)=u″(1)+ku′(1)=0, and the associated special cases corresponding to one or both of h and k equal to infinity. The conditions on the nonlinearity f turn out to be related to the spectrum of the linear boundary value problem u‴=λu′, u(η)=0, u″(0)−hu′(0)=u″(1)+ku′(1)=0, in a natural way.

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.

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