Maagli, HabibToumi, FatenZribi, Malek2020-11-242020-11-242003-05-20Maagli, H., Toumi, F., & Zribi, M. (2003). Existence of positive solutions for some polyharmonic nonlinear boundary-value problems. <i>Electronic Journal of Mathematical Equations, 2003</i>(58), pp. 1-19.1072-6691https://hdl.handle.net/10877/12998We present existence results for the polyharmonic nonlinear elliptic boundary-value problem (-Δ)m u = ƒ(·, u) in B (∂/ ∂v)j u = 0 on ∂B, 0 ≤ j ≤ m - 1. (in the sense of distributions), where B is the unit ball in ℝn and n ≥ 2. The nonlinearity ƒ(x, t) satisfies appropriate conditions related to a Kato class of functions Km,n. Our approach is based on estimates for the polyharmonic Green function with zero Dirichlet boundary conditions and on the Schauder fixed point theorem.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalGreen functionPositive solutionSchauder fixed point theoremSingular polyharmonic elliptic equationArticle