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

Imed Bachar, Habib Màagli, Syrine Masmoudi and Malek Zribi

Abstract and Applied Analysis, 2003, vol. 2003, 1-27

Abstract:

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

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:790938

DOI: 10.1155/S1085337503209039

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