Existence of continuous and singular ground states for semilinear elliptic systems

• Main Author: Cecilia S. Yarur
• Format: Article
• Language: English
• Published: Texas State University 1998-01-01
• Series: Electronic Journal of Differential Equations
• Subjects: Semilinear elliptic systems; ground states.
• Online Access: http://ejde.math.txstate.edu/Volumes/1998/01/abstr.html

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 $$ eqaling{ Delta u(x)+V(|x|)u+a(|x|)v^p &= 0 cr Delta v(x)+V(|x|)v+b(|x|)u^q &= 0,.cr} $$