Abstract
Is there a failure of the inverse function theorem? H. Brezis We will discuss some very natural nonlinear problems, such as $-\Delta u=\lambda e^u$,where the linearized operator is $L=-\Delta - \frac{c}{\mid x \mid}^2$ and $c$ is a small positive constant so that $L$ is invertable. However the nonlinear problem has no solution locally (even in any weak sence)	General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF2 3XF, U.K. Malcom@cs.cf.ac.uk

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