数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1404-1416.doi: 10.1016/S0252-9602(14)60092-8

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COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL

Zagharide Zine EL ABIDINE   

  1. D´epartement de Math´ematiques, Facult´e des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia
  • 收稿日期:2013-06-09 出版日期:2014-09-20 发布日期:2014-09-20

COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL

Zagharide Zine EL ABIDINE   

  1. D´epartement de Math´ematiques, Facult´e des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia
  • Received:2013-06-09 Online:2014-09-20 Published:2014-09-20

摘要:

Let m be a positive integer and B be the unit ball of Rn (≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem
(−Δ)mu = a1(x)uα1 + a2(x)uα2 , lim|x|→1u(x)/(1 − |x|)m−1 = 0,
where α1α2 ∈(−1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.

关键词: Kato class, positive solution, nonlinear polyharmonic equation, asymptotic behavior, schauder fixed point theorem

Abstract:

Let m be a positive integer and B be the unit ball of Rn (≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem
(−Δ)mu = a1(x)uα1 + a2(x)uα2 , lim|x|→1u(x)/(1 − |x|)m−1 = 0,
where α1α2 ∈(−1, 1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.

Key words: Kato class, positive solution, nonlinear polyharmonic equation, asymptotic behavior, schauder fixed point theorem

中图分类号: 

  • 34B27