Existence Results for Polyharmonic Boundary Value Problems in the Unit Ball

Sonia Ben Othman, Habib Mâagli and Malek Zribi

Abstract and Applied Analysis, 2007, vol. 2007, issue 1

Abstract: Here we study the polyharmonic nonlinear elliptic boundary value problem on the unit ball B in ℝn(n ≥ 2)(−△)mu + g(⋅, u) = 0, in B (in the sense of distributions) limx→ξ∈∂B(u(x)/(1−|x|2)m−1)=0(ξ). Under appropriate conditions related to a Kato class on the nonlinearity g(x, t), we give some existence results. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions, including a 3G‐theorem, which leeds to some useful properties on functions belonging to the Kato class.

Date: 2007
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https://doi.org/10.1155/2007/56981

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:056981

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