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dc.contributor.authorMaagli, Habib ( )
dc.contributor.authorToumi, Faten ( Orcid Icon 0000-0002-9923-9729 )
dc.contributor.authorZribi, Malek ( )
dc.identifier.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.en_US

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.

dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectGreen functionen_US
dc.subjectPositive solutionen_US
dc.subjectSchauder fixed point theoremen_US
dc.subjectSingular polyharmonic elliptic equationen_US
dc.titleExistence of positive solutions for some polyharmonic nonlinear boundary-value problemsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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