COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL

doi:10.1016/S0252-9602(14)60092-8

Abstract

Abstract:

Let m be a positive integer and B be the unit ball of Rⁿ (n ≥ 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)u^α^₁ + a₂(x)u^α₂ , lim_|x|→1u(x)/(1 − |x|)^m−1 = 0,
where α₁, α₂ ∈(−1, 1) and a₁, a₂are 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

CLC Number:

34B27

Zagharide Zine EL ABIDINE. COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL[J].Acta mathematica scientia,Series B, 2014, 34(5): 1404-1416.

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