Existence of positive solutions for some polyharmonic nonlinear boundary-value problems
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We 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.
CitationMaagli, H., Toumi, F., & Zribi, M. (2003). Existence of positive solutions for some polyharmonic nonlinear boundary-value problems. Electronic Journal of Mathematical Equations, 2003(58), pp. 1-19.
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