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- Title
SOLUTIONS AND EIGENVALUES OF LAPLACE'S EQUATION ON BOUNDED OPEN SETS.
- Authors
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.
- Subjects
LAPLACE'S equation; POISSON'S equation; GREEN'S functions; INTEGRAL operators; EIGENVALUES
- Publication
Electronic Journal of Differential Equations, 2021, Issue 1-104, p1
- ISSN
1550-6150
- Publication type
Article