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The Existence and Uniqueness of Radial Solutions for Biharmonic Elliptic Equations in an Annulus.
- Source :
-
Axioms (2075-1680) . Jun2024, Vol. 13 Issue 6, p383. 11p. - Publication Year :
- 2024
-
Abstract
- This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵ 2 u = f (| x | , u , | ∇ u | , ▵ u) in an annular domain Ω = { x ∈ R N : r 1 < | x | < r 2 } ( N ≥ 2 ) with the boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : [ r 1 , r 2 ] × R × R + × R → R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ 1 of the Laplace operator − ▵ with boundary condition u | ∂ Ω = 0 , an existence result and a uniqueness result are obtained. The inequality conditions allow for f (r , ξ , ζ , η) to be a superlinear growth on ξ , ζ , η as | (ξ , ζ , η) | → ∞ . Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 178159362
- Full Text :
- https://doi.org/10.3390/axioms13060383