Numerical treatment for boundary value problems of Pantograph functional differential equation using computational intelligence algorithms

2014 ◽  
Vol 24 ◽  
pp. 806-821 ◽  
Author(s):  
Muhammad Asif Zahoor Raja
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Functional Differential Equation ◽  
Computational Intelligence ◽  
Boundary Value ◽  
Numerical Treatment ◽  
Functional Differential

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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