Existence of positive solutions for some polyharmonic nonlinear boundary-value problems
Date
2003-05-20
Authors
Maagli, Habib
Toumi, Faten
Zribi, Malek
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Green function, Positive solution, Schauder fixed point theorem, Singular polyharmonic elliptic equation
Citation
Maagli, 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.
Rights
Attribution 4.0 International