Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one
In this article, we consider a semilinear elliptic equations of the form $Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$. The significance of this result in probability theory is also discussed.
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| Format: | Article |
| Language: | English |
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Texas State University
2006-01-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/09/abstr.html |
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doaj-ae66fba31b60412695e291f877c7a75a2020-11-24T20:58:10ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-01-0120060916Nonexistence of solutions to KPP-type equations of dimension greater than or equal to oneJanos EnglanderPeter L. SimonIn this article, we consider a semilinear elliptic equations of the form $Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$. The significance of this result in probability theory is also discussed.http://ejde.math.txstate.edu/Volumes/2006/09/abstr.htmlKPP-equationsemilinear elliptic equationspositive bounded solutionsbranching Brownian-motion. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Janos Englander Peter L. Simon |
| spellingShingle |
Janos Englander Peter L. Simon Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one Electronic Journal of Differential Equations KPP-equation semilinear elliptic equations positive bounded solutions branching Brownian-motion. |
| author_facet |
Janos Englander Peter L. Simon |
| author_sort |
Janos Englander |
| title |
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one |
| title_short |
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one |
| title_full |
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one |
| title_fullStr |
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one |
| title_full_unstemmed |
Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one |
| title_sort |
nonexistence of solutions to kpp-type equations of dimension greater than or equal to one |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2006-01-01 |
| description |
In this article, we consider a semilinear elliptic equations of the form $Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$. The significance of this result in probability theory is also discussed. |
| topic |
KPP-equation semilinear elliptic equations positive bounded solutions branching Brownian-motion. |
| url |
http://ejde.math.txstate.edu/Volumes/2006/09/abstr.html |
| work_keys_str_mv |
AT janosenglander nonexistenceofsolutionstokpptypeequationsofdimensiongreaterthanorequaltoone AT peterlsimon nonexistenceofsolutionstokpptypeequationsofdimensiongreaterthanorequaltoone |
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