Existence of continuous and singular ground states for semilinear elliptic systems
We study existence results of a curve of continuous and singular ground states for the system $$ eqaling{ -Delta{u} &= {alpha(|x|)}f(v) cr -Delta{v} &= Beta(|x|) g(u),. cr }$$ where $x in R^N setminus {0}$, the functions $f$ and $g$ are increasing Lipschitz continuous functions in $R...
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| Format: | Article |
| Language: | English |
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Texas State University
1998-01-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/1998/01/abstr.html |
| Summary: | We study existence results of a curve of continuous and singular ground states for the system $$ eqaling{ -Delta{u} &= {alpha(|x|)}f(v) cr -Delta{v} &= Beta(|x|) g(u),. cr }$$ where $x in R^N setminus {0}$, the functions $f$ and $g$ are increasing Lipschitz continuous functions in $R$, and $alpha$ and $Beta$ are nonnegative continuous functions in $R^+$. We also study general systems of the form $$ eqaling{ Delta u(x)+V(|x|)u+a(|x|)v^p &= 0 cr Delta v(x)+V(|x|)v+b(|x|)u^q &= 0,.cr} $$ |
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| ISSN: | 1072-6691 |