Geodesic
The fixed point theorem and the boundedness of solutions of differential equations in the Banach space
Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 1-9

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MR Zbl
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.
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.
DOI : 10.21136/MB.1993.126016
Classification : 34C11, 34G20, 47H10, 47H15, 47N20
Keywords: differential equation; Banach space; existence; uniqueness; boundedness; bounded solution; derivative of the norm of a linear mapping; fixed point 
Tumajer, František. The fixed point theorem and the boundedness of solutions of differential equations in the Banach space. Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 1-9. doi: 10.21136/MB.1993.126016
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