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Displaying similar documents to “On the problem of retracting balls onto their boundary.”

The fixed point theorem and the boundedness of solutions of differential equations in the Banach space

František Tumajer (1993)

Mathematica Bohemica

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The properties of solutions of the nonlinear differential equation x ' = A ( s ) x + f ( s , x ) in a Banach space and of the special case of the homogeneous linear differential equation x ' = A ( s ) x are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties.