Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

Ben Othman, Sonia; Mâagli, Habib; Zribi, Malek

doi:https://doi.org/10.1155/2007/56981

Abstract and Applied Analysis

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Volume 2007 | Article ID 056981 | https://doi.org/10.1155/2007/56981

Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

Sonia Ben Othman,¹Habib Mâagli,¹and Malek Zribi¹

Academic Editor: Jean-Pierre Gossez

Received27 Oct 2006

Accepted09 Apr 2007

Published31 May 2007

Abstract

Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in ℝn(n≥2)(−△)mu+g(⋅,u)=0, in B (in the sense of distributions) limx→ξ∈∂B(u(x)/(1−|x|2)m−1)=0(ξ). Under appropriate conditions related to a Kato class on the nonlinearity g(x,t), we give some existence results. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G-theorem, which leeds to some useful properties on functions belonging to the Kato class.

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Copyright © 2007 Sonia Ben Othman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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