Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition
This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the orde...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/564930 |
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| author | Elliot Tonkes |
| author_facet | Elliot Tonkes |
| author_sort | Elliot Tonkes |
| collection | DOAJ |
| description | This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behaviour of solutions to a class of semilinear elliptic equations with a critical Sobolev exponent. |
| format | Article |
| id | doaj-art-d68936aaacf84bd6bdb2c44278633d92 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d68936aaacf84bd6bdb2c44278633d922025-02-03T01:32:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/564930564930Bifurcation of Gradient Mappings Possessing the Palais-Smale ConditionElliot Tonkes0Energy Edge Pty Ltd., P.O. Box 10755, Brisbane, QLD 4000, AustraliaThis paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behaviour of solutions to a class of semilinear elliptic equations with a critical Sobolev exponent.http://dx.doi.org/10.1155/2011/564930 |
| spellingShingle | Elliot Tonkes Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition International Journal of Mathematics and Mathematical Sciences |
| title | Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition |
| title_full | Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition |
| title_fullStr | Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition |
| title_full_unstemmed | Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition |
| title_short | Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition |
| title_sort | bifurcation of gradient mappings possessing the palais smale condition |
| url | http://dx.doi.org/10.1155/2011/564930 |
| work_keys_str_mv | AT elliottonkes bifurcationofgradientmappingspossessingthepalaissmalecondition |