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Keywords:
differential equation; Banach space; existence; uniqueness; boundedness; bounded solution; derivative of the norm of a linear mapping; fixed point
differential equation; Banach space; existence; uniqueness; boundedness; bounded solution; derivative of the norm of a linear mapping; fixed point
Summary:
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.
References:
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