Displaying similar documents to “Measures of noncompactness in the study of solutions of nonlinear differential and integral equations”

Note on measures of noncompactness in Banach sequence spaces.

Jozef Banas, Antonio Martinón (1990)

Extracta Mathematicae

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The notion of a measure of noncompactness turns out to be a very important and useful tool in many branches of mathematical analysis. The current state of this theory and its applications are presented in the books [1,4,11] for example. The notion of a measure of weak noncompactness was introduced by De Blasi [8] and was subsequently used in numerous branches of functional analysis and the theory of differential and integral equations (cf. [2,3,9,10,11], for instance). ...

Trichotomy and bounded solutions of nonlinear differential equations

Mieczysław Cichoń (1994)

Mathematica Bohemica

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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.