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Volume 23, Issue 1
Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

Liping Wang

DOI: 10.4208/jpde.v23.n1.5

J. Part. Diff. Eq., 23 (2010), pp. 80-104.

Published online: 2010-02

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  • 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).

  • Keywords

Infinitely many solutions critical exponent exterior domain

  • AMS Subject Headings

35B40 35B45 35J40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-23-80, author = {Liping Wang }, title = {Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain}, journal = {Journal of Partial Differential Equations}, year = {2010}, volume = {23}, number = {1}, pages = {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).

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v23.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/5223.html} }
TY - JOUR T1 - Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain AU - Liping Wang JO - Journal of Partial Differential Equations VL - 1 SP - 80 EP - 104 PY - 2010 DA - 2010/02 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/5223.html KW - Infinitely many solutions KW - critical exponent KW - exterior domain AB -

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).

Liping Wang . (2010). Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain. Journal of Partial Differential Equations. 23 (1). 80-104. doi:10.4208/jpde.v23.n1.5
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