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
Academic Journal
DOC. TYPE
Article
ABSTRACT
We establish a 3G-theorem for the iterated Green function of (-Δ)pm, (p ≥ 1, m ≥ 1), on the unit ball B of ℝn (n ≥ 1) with boundary conditions (∂/∂ν)j(-Δ)kmu = 0 on ∂B, for 0 ≤ k ≤ p - 1 and 0 ≤ j ≤ 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 (-Δ)pmu = h(·,u), in D (in the sense of distributions), lim∣x∣→1((-Δ)kmu(x)/(1 - ∣x∣)m-1) = 0, for 0 ≤ k ≤ p - 1, where D = B or B\{0} and h is a Borel measurable function on D × (0, ∞) satisfying some appropriate conditions related to Im,n(p).
ACCESSION #
24049422

 

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