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- W4315697816 abstract "Abstract In this article, we study the elliptic system: <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=block> <m:mfenced open={ close=> <m:mrow> <m:mtable displaystyle=true> <m:mtr> <m:mtd columnalign=left> <m:mo>−</m:mo> <m:mi mathvariant=normal>Δ</m:mi> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mo>∣</m:mo> <m:mi>x</m:mi> <m:mspace width=-0.25em /> <m:msup> <m:mrow> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>α</m:mi> </m:mrow> </m:msup> <m:msup> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mi>λ</m:mi> <m:mi>v</m:mi> <m:mo>,</m:mo> </m:mtd> <m:mtd columnalign=left> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=normal>Ω</m:mi> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=left> <m:mo>−</m:mo> <m:mi mathvariant=normal>Δ</m:mi> <m:mi>v</m:mi> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mi>v</m:mi> <m:mo>=</m:mo> <m:mo>∣</m:mo> <m:mi>x</m:mi> <m:mspace width=-0.25em /> <m:msup> <m:mrow> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>α</m:mi> </m:mrow> </m:msup> <m:msup> <m:mrow> <m:mi>v</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:mi>λ</m:mi> <m:mi>u</m:mi> <m:mo>,</m:mo> </m:mtd> <m:mtd columnalign=left> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=normal>Ω</m:mi> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign=left> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>v</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:mo>∂</m:mo> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mfenced> </m:math> left{begin{array}{ll}-Delta u+{mu }_{1}u=| xhspace{-0.25em}{| }^{alpha }{u}^{3}+lambda v,& xin Omega -Delta v+{mu }_{2}v=| xhspace{-0.25em}{| }^{alpha }{v}^{3}+lambda u,& xin Omega u,vgt 0,xin Omega ,u=v=0,xin partial Omega ,end{array}right. where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>⊂</m:mo> <m:msup> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> Omega subset {{mathbb{R}}}^{3} is the unit ball. By the variational method, we prove that if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>α</m:mi> </m:math> alpha is sufficiently small, the ground state solutions of the system are radial symmetric, and if <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>α</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:math> alpha gt 0 is sufficiently large, the ground state solutions are nonradial; however, the solutions are Schwarz symmetry." @default.
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- W4315697816 date "2022-01-01" @default.
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- W4315697816 title "Symmetric results of a Hénon-type elliptic system with coupled linear part" @default.
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- W4315697816 doi "https://doi.org/10.1515/math-2022-0539" @default.
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