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Abstract and Applied Analysis
Volume 2014, Article ID 896902, 11 pages
http://dx.doi.org/10.1155/2014/896902
Research Article

Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity

1Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, China
2School of Mathematics and Information Science, Henan University, Kaifeng 475004, China

Received 3 December 2013; Accepted 26 February 2014; Published 31 March 2014

Academic Editor: Alberto Fiorenza

Copyright © 2014 Baishun Lai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the following semilinear biharmonic equation   , in , and   , on where is the unit ball in and is the exterior unit normal vector. We prove the existence of such that for there exists a minimal (classical) solution , which satisfies . In the extremal case , 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.