Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity

Baishun Lai

Abstract and Applied Analysis, 2014, vol. 2014, 1-11

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:896902

DOI: 10.1155/2014/896902

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