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- W3197529043 abstract "Abstract This paper is concerned with the following Hamiltonian elliptic system <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=block> <m:mfenced open={ close=> <m:mtable columnalign=left left rowspacing=4pt columnspacing=1em> <m:mtr> <m:mtd> <m:mo>−</m:mo> <m:mi mathvariant=normal>Δ</m:mi> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mi>V</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>)</m:mo> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:msub> <m:mi>W</m:mi> <m:mrow> <m:mi>v</m:mi> </m:mrow> </m:msub> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> <m:mo stretchy=false>)</m:mo> <m:mo>,</m:mo> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mrow> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mo>−</m:mo> <m:mi mathvariant=normal>Δ</m:mi> <m:mi>v</m:mi> <m:mo>+</m:mo> <m:mi>V</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>)</m:mo> <m:mi>v</m:mi> <m:mo>=</m:mo> <m:msub> <m:mi>W</m:mi> <m:mrow> <m:mi>u</m:mi> </m:mrow> </m:msub> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>v</m:mi> <m:mo stretchy=false>)</m:mo> <m:mo>,</m:mo> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>x</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mrow> <m:mrow> <m:mi mathvariant=double-struck>R</m:mi> </m:mrow> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mo>,</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:mfenced> </m:math> $$ left{ begin{array}{ll} -Delta u+V(x)u=W_{v}(x, u, v), xin {mathbb{R}}^{N}, -Delta v+V(x)v=W_{u}(x, u, v), xin {mathbb{R}}^{N}, end{array} right. $$ where z = ( u , v ) : ℝ N → ℝ 2 , V ( x ) and W ( x , z ) are 1-periodic in x . By making use of variational approach for strongly indefinite problems, we obtain a new existence result of nontrivial solution under new conditions that the nonlinearity <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>W</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>z</m:mi> <m:mo stretchy=false>)</m:mo> <m:mo>:=</m:mo> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:msub> <m:mi>V</m:mi> <m:mrow> <m:mi mathvariant=normal>∞</m:mi> </m:mrow> </m:msub> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo stretchy=false>)</m:mo> <m:mrow> <m:mo>|</m:mo> </m:mrow> <m:mi>A</m:mi> <m:mi>z</m:mi> <m:msup> <m:mrow> <m:mo>|</m:mo> </m:mrow> <m:mn>2</m:mn> </m:msup> <m:mo>+</m:mo> <m:mi>F</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>z</m:mi> <m:mo stretchy=false>)</m:mo> </m:math> $ W(x,z):=frac{1}{2}V_{infty}(x)|Az|^2+F(x, z) $ is general asymptotically quadratic, where V ∞ ( x ) ∈ (ℝ N , ℝ) is 1-periodic in x and inf ℝ N V ∞ ( x ) > min ℝ N V ( x ), and A is a symmetric non-negative definite matrix." @default.
- W3197529043 created "2021-09-13" @default.
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- W3197529043 date "2021-09-03" @default.
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- W3197529043 title "New asymptotically quadratic conditions for Hamiltonian elliptic systems" @default.
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