scholarly journals A periodic boundary value problem in Hilbert space

1994 ◽  
Vol 119 (4) ◽  
pp. 347-358
Author(s):  
Boris Rudolf
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem

scholarly journals On a Periodic Boundary Value Problem for Fractional Quasilinear Differential Equations with a Self-Adjoint Positive Operator in Hilbert Spaces

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 219
Author(s):  
Mikhail Kamenskii ◽  
Garik Petrosyan ◽  
Paul Raynaud de Fitte ◽  
Jen-Chih Yao
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Mild Solution ◽  
Positive Operator ◽  
Hilbert Spaces ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Linear Part ◽  
Periodic Boundary Value Problem

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.

scholarly journals Rapid Convergence of Solution for Hybrid System with Causal Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Peiguang Wang ◽  
Zhifang Li ◽  
Yonghong Wu
Keyword(s):  
Boundary Value Problem ◽  
Hybrid System ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Periodic Boundary Value Problem ◽  
Rapid Convergence ◽  
Causal Operators ◽  
Convergence Of Solution

We investigated the convergence of iterative sequences of approximate solutions to a class of periodic boundary value problem of hybrid system with causal operators and established two sequences of approximate solutions that converge to the solution of the problem with rate of orderk≥2.

Sign in / Sign up

Export Citation Format

Share Document