TITLE

# ESTIMATES FOR THE GREEN FUNCTION AND EXISTENCE OF POSITIVE SOLUTIONS FOR HIGHER-ORDER ELLIPTIC EQUATIONS

AUTHOR(S)
Bachar, Imed
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We establish a 3G-theorem for the iterated Green function of (-Î”)pm, (p â‰¥ 1, m â‰¥ 1), on the unit ball B of â„n (n â‰¥ 1) with boundary conditions (âˆ‚/âˆ‚Î½)j(-Î”)kmu = 0 on âˆ‚B, for 0 â‰¤ k â‰¤ p - 1 and 0 â‰¤ j â‰¤ m - 1.We exploit this result to study a class of potentials Jm,n(p). Next, we aim at proving the existence of positive continuous solutions for the following polyharmonic nonlinear problems (-Î”)pmu = h(Â·,u), in D (in the sense of distributions), limâˆ£xâˆ£â†’1((-Î”)kmu(x)/(1 - âˆ£xâˆ£)m-1) = 0, for 0 â‰¤ k â‰¤ p - 1, where D = B or B\{0} and h is a Borel measurable function on D Ã— (0, âˆž) satisfying some appropriate conditions related to Im,n(p).
ACCESSION #
24049422

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