ESTIMATES ON THE GREEN FUNCTION AND EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR POLYHARMONIC PROBLEMS OUTSIDE THE UNIT BALL

Author:

BACHAR IMED1,MÂAGLI HABIB1,ZEDDINI NOUREDDINE1

Affiliation:

1. Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia

Abstract

Let [Formula: see text] be the Green function of (-Δ)m, m ≥ 1, on the complementary D of the unit closed ball in ℝn, n ≥ 2, with Dirichlet boundary conditions [Formula: see text], 0 ≤ j ≤ m - 1. We establish some estimates on [Formula: see text] including the 3G-Inequality given by (1.3). Next, we introduce a polyharmonic Kato class of functions [Formula: see text] and we exploit the properties of this class to study the existence of positive solutions of some polyharmonic nonlinear elliptic problems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

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