Open AccessON THE OSCILLATION OF AN ELLIPTIC EQUATION OF FOURTH ORDER
Author(s) -
Bhagat Singh
Publication year - 1996
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.27.1996.4353
Subject(s) - mathematics , oscillation (cell signaling) , order (exchange) , elliptic curve , domain (mathematical analysis) , mathematical analysis , omega , laplace's equation , operator (biology) , mathematical physics , physics , differential equation , chemistry , quantum mechanics , biochemistry , finance , repressor , transcription factor , economics , gene
The elliptic equation\[\Delta^2 u(|x|)+g(|x|)u(|x|)=f(|x|)\]is studied for its oscillatory behavior. $\Delta$ is the Laplace operator. Sufficient condi tions have been found to ensure that all solutions of this equation continuable in some exterior domain $\Omega=\{x=(x_1, x_2, x_3):|x|>A\}$ where $|x|=(\sum_{i=1}^3 x_i^2)^{1/2}$ are oscillatory.