scholarly journals A Class of Linear Boundary Value Problem for $k$-regular Functions in Clifford Analysis

2016 ◽  
Vol 8 (3) ◽  
pp. 57
Author(s):  
Yan Zhang
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Regular Function ◽  
Integral Equation Method ◽  
Linear Boundary ◽  
Regular Functions ◽  
Linear Boundary Value Problem

In this paper, we introduce the linear boundary value problem for $k$-regular function, and give an unique solution for this problem by integral equation method and fixed-point theorem.

scholarly journals The Boundary Value Problem with Haseman-shift for k-regular Functions on Unbounded Domains in Clifford Analysis

2016 ◽  
Vol 8 (1) ◽  
pp. 38
Author(s):  
Yan Zhang
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Regular Function ◽  
Unbounded Domains ◽  
Regular Functions

In this paper, we introduce the boundary value problem with Haseman shift for $k$-regular function on unbounded domains, and give the unique solution for this problem by integral equation<br />method and fixed-point theorem.

scholarly journals A Boundary Value Problem for Bihypermonogenic Functions in Clifford Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoli Bian ◽  
Yuying Qiao
Keyword(s):  
Boundary Value Problem ◽  
Unique Solution ◽  
Clifford Analysis ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Linear Boundary ◽  
Plemelj Formula ◽  
Linear Boundary Value Problem

This paper deals with a nonlinear boundary value problem for bihypermonogenic functions in Clifford analysis. The integrals of quasi-Cauchy’s type and Plemelj formula for bihypermonogenic functions are firstly reviewed briefly. The nonlinear Riemmann boundary value problem for bihypermonogenic functions is discussed and the existence of solutions is obtained, which also indicates that the linear boundary value problem has a unique solution.

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.

Sign in / Sign up

Export Citation Format

Share Document