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- W2145812500 abstract "We study, the existence and uniqueness of the initial value problems in a Banach space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$E$ id=E1><mml:mi>E</mml:mi></mml:math>for the abstract nonlinear differential equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$({d^{n - 1}}/{dt^{n - 1}})({du}/{dt} + Au) = B(t)u + f(t,W(t))$ id=E2><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>d</mml:mi><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>u</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mi>u</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>W</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations." @default.
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- W2145812500 date "2001-01-01" @default.
- W2145812500 modified "2023-09-26" @default.
- W2145812500 title "On the correct formulation of a nonlinear differential equations in Banach space" @default.
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- W2145812500 doi "https://doi.org/10.1155/s0161171201002307" @default.
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