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The Existence and Uniqueness of Radial Solutions for Biharmonic Elliptic Equations in an Annulus
- Source :
- Axioms, Vol 13, Iss 6, p 383 (2024)
- Publication Year :
- 2024
- Publisher :
- MDPI AG, 2024.
-
Abstract
- This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵2u=f(|x|,u,|∇u|,▵u) in an annular domain Ω={x∈RN:r1<|x|<r2}(N≥2) with the boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:[r1,r2]×R×R+×R→R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ1 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.
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 6
- Database :
- Directory of Open Access Journals
- Journal :
- Axioms
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.b3d0f121effa4c4eb3db161058b30541
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/axioms13060383