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- W3028674014 abstract "Abstract Let $T > 1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>T</mml:mi><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math> be an integer, and let $mathbb{T}={1, 2,ldots ,T}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mo>{</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>}</mml:mo></mml:math> . We show the existence of positive solutions of the Dirichlet boundary value problem with second-order difference operator $$ textstylebegin{cases} -triangle ^{2} u(j-1)=lambda f(j, u(j)), quad jin mathbb{T}, u(0)=u(T + 1)=0, end{cases} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mo>{</mml:mo><mml:mtable><mml:mtr><mml:mtd><mml:mo>−</mml:mo><mml:msup><mml:mi>△</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mi>u</mml:mi><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mspace /><mml:mi>j</mml:mi><mml:mo>∈</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>u</mml:mi><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>u</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math> where $lambda >0$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>λ</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn></mml:math> is a parameter, and $f:mathbb{T}times mathbb{R} ^{+}to mathbb{R}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>f</mml:mi><mml:mo>:</mml:mo><mml:mi>T</mml:mi><mml:mo>×</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>R</mml:mi></mml:math> is a continuous function satisfying $f(j, 0)<0$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo><mml:mo><</mml:mo><mml:mn>0</mml:mn></mml:math> for all $jin mathbb{T}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>j</mml:mi><mml:mo>∈</mml:mo><mml:mi>T</mml:mi></mml:math> . The proofs of the main results are based upon topological degree and global bifurcation techniques." @default.
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- W3028674014 date "2020-02-11" @default.
- W3028674014 modified "2023-09-24" @default.
- W3028674014 title "Positive solutions for some discrete semipositone problems via bifurcation theory" @default.
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- W3028674014 doi "https://doi.org/10.1186/s13662-020-2494-5" @default.
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