Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball



Abstract and Applied Analysis

Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

Sonia Ben Othman, Habib Mâagli, and Malek Zribi

Source: Abstr. Appl. Anal. Volume 2007 (2007), 16 pages.

Abstract

Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball $B$ in $\mathbb{R}^n (n\ge 2)(-\Delta)^m u + g(\cdot , u) =0$ $$, in $B$ (in the sense of distributions) $\lim_{x \to \zeta\in \partial B}(u(x) / (1- | x|^2 )^{m-1})= 0 {\zeta}$. 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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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aaa/1183666878
Digital Object Identifier: doi:10.1155/2007/56981


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