Acta mathematica scientia,Series A ›› 2004, Vol. 24 ›› Issue (3): 354-361.

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Existence and Uniqueness of Positive Solutions for a Class ofElliptic Problems
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 DAN Qi-Kang   

  • Online:2004-06-22 Published:2004-06-22
  • Supported by:

    国家自然科学基金(10371021)资助

Abstract:

In this paper, the author studies the existence and uniqueness of positive solutions for the quasilinear elliptic problem$$u|\-\{Ω=0: -div[(d+|u|\+2)\+\{〖SX(〗p〖〗2〖SX)〗-1u]=λ\-1u\+\{p-1+g(x,u)〓 x∈Ω,$$where $Ω$ is a bounded domain in $R\+N,λ\-1$ is the firsteigenvalue of $△\-P$ on $Ω$ subject to zero Dirichlet boundary conditions, and $g(x,t)$satisfies the growth condition $ lim[DD(X]t→+∞[DD)]〖SX(〗g(x,t)〖〗t\+\{p-1〖SX)〗=0, p>1, 0≤d<+∞.$

CLC Number: 

  • 36J65
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