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, Volume 113, Issue 3, pp 269–291 | Cite as

Estimates on the Green function and existence of positive solutions for some polyharmonic nonlinear equations in the half space

  • Imed Bachar
  • Habib MâagliEmail author
  • Malek Zribi


Let G m,n be the Green function of with Dirichlet boundary conditions We establish some estimates on G m,n , including a 3G-Theorem. Next, we introduce a Kato class of functions and we exploit properties of these functions to study the existence of positive solutions of some m-polyharmonic nonlinear elliptic problems.


Nonlinear Equation Green Function Half Space 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Département de MathématiquesFaculté des Sciences de Tunis, Campus UniversitaireTunisTunisia

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