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• W2804670259 abstract "Abstract We study the following coupled elliptic system with critical nonlinearities: <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo>{</m:mo> <m:mtable columnspacing=0pt displaystyle=true rowspacing=0pt> <m:mtr> <m:mtd /> <m:mtd columnalign=left> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mrow> <m:mi mathvariant=normal>△</m:mi> <m:mo>⁢</m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mrow> <m:mi>f</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo>⁢</m:mo> <m:mi>h</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:mi>K</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>v</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> <m:mtd /> <m:mtd columnalign=right> <m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>N</m:mi> </m:msup> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> </m:mtr> <m:mtr> <m:mtd /> <m:mtd columnalign=left> <m:mrow> <m:mrow> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mrow> <m:mi mathvariant=normal>△</m:mi> <m:mo>⁢</m:mo> <m:mi>v</m:mi> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mi>v</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mrow> <m:mi>g</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>v</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>β</m:mi> <m:mo>⁢</m:mo> <m:mi>H</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:mi>k</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>v</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> <m:mtd /> <m:mtd columnalign=right> <m:mrow> <m:mrow> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>N</m:mi> </m:msup> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> </m:mtr> <m:mtr> <m:mtd /> <m:mtd columnalign=left> <m:mrow> <m:mrow> <m:mrow> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mrow> <m:msup> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>N</m:mi> </m:msup> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:math> left{begin{aligned} &displaystyle-triangle{u}+u=f(u)+beta h(u)K(v),&&% displaystyle xin{mathbb{R}}^{N}, &displaystyle-triangle{v}+v=g(v)+beta H(u)k(v),&&displaystyle xin{mathbb% {R}}^{N}, &displaystyle u,vin H^{1}({mathbb{R}}^{N}),end{aligned}right. where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>β</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {beta>0} ; f , g are differentiable functions with critical growth; and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>H</m:mi> <m:mo>,</m:mo> <m:mi>K</m:mi> </m:mrow> </m:math> {H,K} are primitive functions of h and k , respectively. Under some assumptions on f , g , h and k , we obtain the existence of a positive ground state solution of this system for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>N</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {Ngeq 2} ." @default.
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• W2804670259 date "2017-06-21" @default.
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• W2804670259 title "Ground State for a Coupled Elliptic System with Critical Growth" @default.
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