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

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Abstract.

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.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060, Tunis, Tunisia

    Imed Bachar, Habib Mâagli & Malek Zribi

Authors
  1. Imed Bachar
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  2. Habib Mâagli
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  3. Malek Zribi
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Correspondence to Habib Mâagli.

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Mathematics Subject Classification (2000): 34B27, 35J40

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Bachar, I., Mâagli, H. & Zribi, M. Estimates on the Green function and existence of positive solutions for some polyharmonic nonlinear equations in the half space. manuscripta math. 113, 269–291 (2004). https://doi.org/10.1007/s00229-003-0410-4

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  • DOI: https://doi.org/10.1007/s00229-003-0410-4

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