Year: 2010
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 1 : pp. 80–104
Abstract
We consider the following nonlinear problem -Δu=u^{\frac{N+2}{N-2}}, u > 0, in R^N\Ω, u(x)→ 0, as |x|→+∞, \frac{∂u}{∂n}=0, on ∂Ω, where Ω⊂R^N N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of ∂Ω. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside (with some symmetries).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v23.n1.5
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 1 : pp. 80–104
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Infinitely many solutions
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