On the correct formulation of a nonlinear differential equation in Banach spaces (Q5954801)
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scientific article; zbMATH DE number 1702012
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the correct formulation of a nonlinear differential equation in Banach spaces |
scientific article; zbMATH DE number 1702012 |
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On the correct formulation of a nonlinear differential equation in Banach spaces (English)
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10 December 2002
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initial value problem
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nonlinear differential equation
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0.94247687
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0.92731065
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0.91347766
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Here, using the Banach contraction principle, the authors prove existence and uniqueness of solutions to initial value problems for the nonlinear differential equation NEWLINE\[NEWLINE\frac{d^{n-1}}{dt^{n-1}}(\frac{du}{dt}+Au)=B(t)u+f(t,W),NEWLINE\]NEWLINE considered in a Banach space. The continuous dependence of a solution on the initial conditions is established. An application to partial differential equations is also presented.
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