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Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

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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