Hadamard types of well-posedness of non-self set-valued mappings for coincide points

2005 ◽  
Vol 63 (5-7) ◽  
pp. e2427-e2436 ◽  
Author(s):  
Yong-hui Zhou ◽  
Jian Yu ◽  
Hui Yang ◽  
Shu-wen Xiang
Keyword(s):  
Well Posedness ◽  
Set Valued Mappings

On Nadler type results in ultrametric spaces with application to well-posedness

2017 ◽  
Vol 10 (04) ◽  
pp. 1750073 ◽  
Author(s):  
M. Pitchaimani ◽  
D. Ramesh Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Ultrametric Spaces ◽  
Common Fixed Point Problem ◽  
Set Valued Mappings

In this paper, we generalize Nadler’s result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler’s type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

scholarly journals The BV solution of the parabolic equation with degeneracy on the boundary

2016 ◽  
Vol 14 (1) ◽  
pp. 272-282
Author(s):  
Huashui Zhan ◽  
Shuping Chen
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Well Posedness ◽  
Test Functions ◽  
The Stability

AbstractConsider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

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