The singular extremal solutions of the bi-Laplacian with exponential nonlinearity
نویسندگان
چکیده
منابع مشابه
The singular extremal solutions of the bilaplacian with exponential nonlinearity
Consider the problem ∆u = λe in B u = ∂u ∂n = 0 on ∂B, where B is the unit ball in R and λ is a parameter. Unlike the Gelfand problem the natural candidate u = −4 ln(|x|), for the extremal solution, does not satisfy the boundary conditions and hence showing the singular nature of the extremal solution in large dimensions close to the critical dimension is challenging. Dávila et al. in [5] use...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-10257-5