Existence and asymptotic behavior of ground state solutions of semilinear elliptic system
Existence and asymptotic behavior of ground state solutions of semilinear elliptic system
Abstract In this article, we take up the existence and the asymptotic behavior of entire bounded positive solutions to the following semilinear elliptic system: -Δ u = <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>a</m:mi><m:mn>1</m:mn></m:msub></m:math> a_{1} ( x ) <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>u</m:mi><m:mi>α</m:mi></m:msup></m:math> u^{\alpha} <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>v</m:mi><m:mi>r</m:mi></m:msup></m:math> v^{r} , x <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mo>∈</m:mo></m:math> \in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>ℝ</m:mi><m:mi>n</m:mi></m:msup></m:math> \mathbb{R}^{n} ( n <m:math …