On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle

2015 ◽  
Vol 6 (3) ◽  
Author(s):  
Makhmud A. Sadybekov ◽  
Batirkhan K. Turmetov ◽  
Berikbol T. Torebek
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Explicit Form ◽  
Laplace Operator ◽  
Green's Function ◽  
Robin Problem ◽  
The Green Function ◽  
The Laplace Operator

AbstractThe paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ

On Green’s function of the Robin problem for the Poisson equation

2019 ◽  
Vol 10 (3) ◽  
pp. 203-213 ◽  
Author(s):  
Valery V. Karachik ◽  
Batirkhan K. Turmetov
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Unit Ball ◽  
Poisson Equation ◽  
Green's Function ◽  
Explicit Representation ◽  
Robin Problem ◽  
The Poisson Equation ◽  
The Green Function

AbstractAn explicit representation of the Green function of the Robin problem for the Poisson equation in the unit ball is given.

scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

scholarly journals Pointwise bounds for the Green's function for the Neumann-Laplace operator in $ \text{R}^3 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Hoff
Keyword(s):  
Sobolev Space ◽  
Green’S Function ◽  
Laplace Operator ◽  
Green's Function ◽  
Neumann Boundary ◽  
Space Theory ◽  
Basic Facts ◽  
The Laplace Operator ◽  
Bounded Sets ◽  
Scaling Arguments

<p style='text-indent:20px;'>We derive pointwise bounds for the Green's function and its derivatives for the Laplace operator on smooth bounded sets in <inline-formula><tex-math id="M2">\begin{document}$ {\bf R}^3 $\end{document}</tex-math></inline-formula> subject to Neumann boundary conditions. The proofs require only ordinary calculus, scaling arguments and the most basic facts of <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-Sobolev space theory.</p>

Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential

2017 ◽  
Vol 121 (2) ◽  
pp. 263 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Positive Solution ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Type Theorem ◽  
Robin Problem ◽  
Continuity Properties ◽  
Superlinear Growth ◽  
Unbounded Potential ◽  
Carathéodory Function ◽  
The Laplace Operator

We consider a parametric Robin problem driven by the Laplace operator plus an indefinite and unbounded potential. The reaction term is a Carathéodory function which exhibits superlinear growth near $+\infty $ without satisfying the Ambrosetti-Rabinowitz condition. We are looking for positive solutions and prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. We also establish the existence of the minimal positive solution $u^*_{\lambda }$ and investigate the monotonicity and continuity properties of the map $\lambda \mapsto u^*_{\lambda }$.

Green function or green's function?

2006 ◽  
Vol 2 (10) ◽  
pp. 646-646 ◽  
Author(s):  
M. C. M. Wright
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function
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