Existence of blowup solutions for nonlinear problems with a gradient term
We prove the existence of positive explosive solutions for the equation Δu+λ(|x|)|∇u(x)|=ϕ(x,u(x)) in the whole space ℝN(N≥3), where λ:[0,∞)→[0,∞) is a continuous function and ϕ:ℝN×[0,∞)→[0,∞) is required to satisfy some hypotheses detailed below. More precisely, we will give a necessary and suffici...
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Hindawi Limited
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/80605 |
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doaj-5b6837d4ec684cb68ab994c43dbe3fc42020-11-24T21:42:16ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/8060580605Existence of blowup solutions for nonlinear problems with a gradient termFaten Toumi0Département des Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, TunisiaWe prove the existence of positive explosive solutions for the equation Δu+λ(|x|)|∇u(x)|=ϕ(x,u(x)) in the whole space ℝN(N≥3), where λ:[0,∞)→[0,∞) is a continuous function and ϕ:ℝN×[0,∞)→[0,∞) is required to satisfy some hypotheses detailed below. More precisely, we will give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.http://dx.doi.org/10.1155/IJMMS/2006/80605 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Faten Toumi |
| spellingShingle |
Faten Toumi Existence of blowup solutions for nonlinear problems with a gradient term International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Faten Toumi |
| author_sort |
Faten Toumi |
| title |
Existence of blowup solutions for nonlinear problems with a gradient term |
| title_short |
Existence of blowup solutions for nonlinear problems with a gradient term |
| title_full |
Existence of blowup solutions for nonlinear problems with a gradient term |
| title_fullStr |
Existence of blowup solutions for nonlinear problems with a gradient term |
| title_full_unstemmed |
Existence of blowup solutions for nonlinear problems with a gradient term |
| title_sort |
existence of blowup solutions for nonlinear problems with a gradient term |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2006-01-01 |
| description |
We prove the existence of positive explosive solutions for the
equation Δu+λ(|x|)|∇u(x)|=ϕ(x,u(x)) in the whole space ℝN(N≥3), where λ:[0,∞)→[0,∞) is a continuous function and ϕ:ℝN×[0,∞)→[0,∞) is
required to satisfy some hypotheses detailed below. More
precisely, we will give a necessary and sufficient condition for
the existence of a positive solution that blows up at infinity. |
| url |
http://dx.doi.org/10.1155/IJMMS/2006/80605 |
| work_keys_str_mv |
AT fatentoumi existenceofblowupsolutionsfornonlinearproblemswithagradientterm |
| _version_ |
1725917951558680576 |