Geodesic
Trichotomy and bounded solutions of nonlinear differential equations
Mathematica Bohemica, Tome 119 (1994) no. 3, pp. 275-284.

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The existence of bounded solutions for equations $x'=A(t)x+f(t,x)$ in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation $f$ satisfies some conditions expressed in terms of measures of noncompactness.
DOI : 10.21136/MB.1994.126161
Classification : 34C11, 34C28, 34G20, 47H15, 47N20
Keywords: existence; bounded solutions; quasilinear differential; trichotomy; measures of noncompactness; Banach spaces 
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Cichoń, Mieczysław. Trichotomy and bounded solutions of nonlinear differential equations. Mathematica Bohemica, Tome 119 (1994) no. 3, pp. 275-284. doi : 10.21136/MB.1994.126161. http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126161/

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