Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Second Order Functional-Differential Equation

2021 ◽  
Vol 65 (12) ◽  
pp. 1-5
Author(s):  
G. E. Abduragimov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Second Order ◽  
Functional Differential

scholarly journals Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
E. M. Hamdallah ◽  
Kh. W. El-kadeky
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Nonlocal Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Second Order ◽  
Nonlocal Boundary Value Problem ◽  
Functional Differential

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equationx′′(t)=f(t,x(ϕ(t))),t∈(0,1), with the nonlocal condition∑k=1makx(τk)=x0,x′(0)+∑j=1nbjx′(ηj)=x1, whereτk∈(a,d)⊂(0,1),ηj∈(c,e)⊂(0,1), andx0,x1>0. As an application the integral and the nonlocal conditions∫adx(t)dt=x0,x′(0)+x(e)-x(c)=x1will be considered.

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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