Abstract and Applied Analysis

Estimates for the Green function and singular solutions for polyharmonic nonlinear equation

Imed Bachar, Habib Mâagli, Syrine Masmoudi, and Malek Zribi

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Abstract

We establish a new form of the 3G theorem for polyharmonic Green function on the unit ball of n(n2) corresponding to zero Dirichlet boundary conditions. This enables us to introduce a new class of functions Km,n containing properly the classical Kato class Kn. We exploit properties of functions belonging to Km,n to prove an infinite existence result of singular positive solutions for nonlinear elliptic equation of order 2m.

Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 12 (2003), 715-741.

Dates
First available in Project Euclid: 3 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1057257795

Digital Object Identifier
doi:10.1155/S1085337503209039

Mathematical Reviews number (MathSciNet)
MR1995485

Zentralblatt MATH identifier
1129.35348

Subjects
Primary: 34B27: Green functions 35J40

Citation

Bachar, Imed; Mâagli, Habib; Masmoudi, Syrine; Zribi, Malek. Estimates for the Green function and singular solutions for polyharmonic nonlinear equation. Abstr. Appl. Anal. 2003 (2003), no. 12, 715--741. doi:10.1155/S1085337503209039. https://projecteuclid.org/euclid.aaa/1057257795


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