Convergence of collocation methods for solving periodic boundary value problems for renewal equations defined through finite‐dimensional boundary conditions

2021 ◽  
Author(s):  
Alessia Andó
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Collocation Methods ◽  
Renewal Equations ◽  
Finite Dimensional ◽  
Periodic Boundary Value Problems ◽  
Dimensional Boundary

scholarly journals On some analogues of periodic problems for Laplace equation with an oblique derivative under boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
pp. 13-27
Author(s):  
Batirkhan Turmetov ◽  
Maira Koshanova ◽  
Moldir Muratbekova
Keyword(s):  
Dirichlet Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Laplace Equation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Periodic Boundary Value Problems ◽  
Periodic Problems ◽  
Sequential Solution

AbstractIn this paper, we study solvability of new classes of nonlocal boundary value problems for the Laplace equation in a ball. The considered problems are multidimensional analogues (in the case of a ball) of classical periodic boundary value problems in rectangular regions. To study the main problem, first, for the Laplace equation, we consider an auxiliary boundary value problem with an oblique derivative. This problem generalizes the well-known Neumann problem and is conditionally solvable. The main problems are solved by reducing them to sequential solution of the Dirichlet problem and the problem with an oblique derivative. It is proved that in the case of periodic conditions, the problem is conditionally solvable; and in this case the exact condition for solvability of the considered problem is found. When boundary conditions are specified in the anti-periodic conditions form, the problem is certainly solvable. The obtained general results are illustrated with specific examples.

scholarly journals Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Chatthai Thaiprayoon ◽  
Decha Samana ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Jump Conditions ◽  
Comparison Result ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Minimal And Maximal Solutions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

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