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2007 Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball
Sonia Ben Othman, Habib Mâagli, Malek Zribi
Abstr. Appl. Anal. 2007: 1-16 (2007). DOI: 10.1155/2007/56981

Abstract

Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in n ( n 2 ) ( ) m u + g ( , u ) = 0 , in B (in the sense of distributions) lim x 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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Sonia Ben Othman. Habib Mâagli. Malek Zribi. "Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball." Abstr. Appl. Anal. 2007 1 - 16, 2007. https://doi.org/10.1155/2007/56981

Information

Published: 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1157.35379
MathSciNet: MR2320800
Digital Object Identifier: 10.1155/2007/56981

Rights: Copyright © 2007 Hindawi

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