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On nonlinear differential equations in generalized Musielak-Orlicz spaces

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider ordinary differential equations u′(t)+(I−T)u(t)=0, where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and T is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.
Rocznik
Strony
13--33
Opis fizyczny
Bibliogr. 68 poz.
Twórcy
  • School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Bibliografia
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Bibliografia
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