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

Author

Listed:
  • Imed Bachar
  • Habib Màagli
  • Syrine Masmoudi
  • Malek Zribi

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 .

Suggested Citation

  • Imed Bachar & Habib Màagli & Syrine Masmoudi & Malek Zribi, 2003. "Estimates for the Green function and singular solutions for polyharmonic nonlinear equation," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-27, January.
    • Handle: RePEc:hin:jnlaaa:790938
    DOI: 10.1155/S1085337503209039
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