College of Applied Mathematics
Chengdu University of Information Technology
Chengdu, Sichuan 610225, China
email: gcyang@cuit.edu.cn
Department of Mathematics
Ryerson University
Toronto, Ontario, Canada M5B 2K3
email: klan@ryerson.ca
Guangchong Yang, Kunquan Lan
Abstract:
We obtain solutions for Laplace's and Poisson's equations on
bounded open subsets of
Rn, (n≥2), via Hammerstein integral operators involving
kernels and Green's functions, respectively.
The new solutions are different from the previous ones obtained
by the well-known Newtonian potential kernel and the Newtonian potential operator.
Our results on eigenvalue problems of Laplace's equation
are different from the previous results that use the Newtonian potential operator and
require n≥3.
As a special case of the eigenvalue problems, we provide a result under
an easily verifiable condition on the weight function when n≥3.
This result cannot be obtained by using the Newtonian potential operator.
Submitted July 12, 2021. Published October 18, 2021.
Math Subject Classifications: 35J05, 31A05, 31B05, 35J08, 47A75.
Key Words: Eigenvalue; Laplace's equation; Poisson's equation; Green's function;
Hammerstein integral operator.
DOI: https://doi.org/10.58997/ejde.2021.87
Show me the PDF file (355 KB), TEX file for this article.
|
Guangchong Yang College of Applied Mathematics Chengdu University of Information Technology Chengdu, Sichuan 610225, China email: gcyang@cuit.edu.cn |
|---|---|
|
Kunquan Lan Department of Mathematics Ryerson University Toronto, Ontario, Canada M5B 2K3 email: klan@ryerson.ca |
Return to the EJDE web page