On one class of integro-differential equations (Q2719410)
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scientific article; zbMATH DE number 1609664
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On one class of integro-differential equations |
scientific article; zbMATH DE number 1609664 |
Statements
25 June 2001
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integro-differential equation
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existence
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nonlinear
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continuously differentiable solution
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0.95618093
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0.95136994
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0.94596964
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0.94405216
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On one class of integro-differential equations (English)
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For the solution of the integro-differential equation NEWLINE\[NEWLINE \dot x(t) = F\Biggl(t,x(t), \int_0^t K(t,s,x(s)) ds, \int_0^T H(t,s,x(s)) ds\Biggr)\tag{1} NEWLINE\]NEWLINE with initial condition NEWLINE\[NEWLINE x(0)=x_0\tag{2} NEWLINE\]NEWLINE existence and uniqueness conditions are established on the segment \(\Delta\) in the class of continuously differentiable functions.
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