Volume 2, Issue 4
Positive Solutions of {Delta u}+u^{(n+2)/(n-2)}=0 on Contractible Domains

Ding Weiyue

J. Part. Diff. Eq.,2(1989),pp.83-88

Published online: 1989-02

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  • Abstract
We show that there are bounded contractible domains in R^n, n ≥ 3, on which the Dirichlet problem for the equation Δu +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem.
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@Article{JPDE-2-83, author = {}, title = {Positive Solutions of {Delta u}+u^{(n+2)/(n-2)}=0 on Contractible Domains}, journal = {Journal of Partial Differential Equations}, year = {1989}, volume = {2}, number = {4}, pages = {83--88}, abstract = { We show that there are bounded contractible domains in R^n, n ≥ 3, on which the Dirichlet problem for the equation Δu +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem. }, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5845.html} }
TY - JOUR T1 - Positive Solutions of {Delta u}+u^{(n+2)/(n-2)}=0 on Contractible Domains JO - Journal of Partial Differential Equations VL - 4 SP - 83 EP - 88 PY - 1989 DA - 1989/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5845.html KW - AB - We show that there are bounded contractible domains in R^n, n ≥ 3, on which the Dirichlet problem for the equation Δu +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem.
Ding Weiyue. (1970). Positive Solutions of {Delta u}+u^{(n+2)/(n-2)}=0 on Contractible Domains. Journal of Partial Differential Equations. 2 (4). 83-88. doi:
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