Some Remarks on Biharmonic Elliptic Problems with a Singular Nonlinearity - Baishun Lai (Abstract and Applied Analysis)
We study the following semilinear biharmonic equation  , 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.