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- W1970590993 abstract "A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$L_{2}(Omega) times C(0,T)$ id=E1><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ω</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mi>C</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Omega = {(x,y): sqrt{x^{2} + y^{2}} leq a}$ id=E2><mml:mrow><mml:mi>Ω</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>:</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mo>≤</mml:mo><mml:mi>a</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$z = 0$ id=E3><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$T < infty$ id=E4><mml:mrow><mml:mi>T</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math>. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$C([Omega] times [Omega])$ id=E5><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mi>Ω</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi>Ω</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, while the kernel of Volterra integral term is a positive and continuous function that belongs to the class<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$C[0,T]$ id=E6><mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:math>. Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established in the paper." @default.
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- W1970590993 date "2001-01-01" @default.
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- W1970590993 title "Fredholm-Volterra integral equation with potential kernel" @default.
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- W1970590993 doi "https://doi.org/10.1155/s0161171201005981" @default.
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