Open Access
2014 Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity
Baishun Lai
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/896902


We study the following semilinear biharmonic equation Δ2u=λ/1-u , in 𝔹, and u=u/n=0, on 𝔹, where 𝔹 is the unit ball in n and n is the exterior unit normal vector. We prove the existence of λ*>0 such that for λ(0,λ*) there exists a minimal (classical) solution u̲λ, which satisfies 0<u̲λ<1. In the extremal case λ=λ*, we prove the existence of a weak solution which is the unique solution even in a very weak sense. Besides, several new difficulties arise and many problems still remain to be solved. We list those of particular interest in the final section.


Download Citation

Baishun Lai. "Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity." Abstr. Appl. Anal. 2014 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023266
MathSciNet: MR3193556
Digital Object Identifier: 10.1155/2014/896902

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top