On nonlinear differential equations in generalized Musielak-Orlicz spaces

• Autorzy: Kozlowski W. M.

Identyfikatory

DOI

10.14708/cm.v53i2.779

• 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.

Słowa kluczowe

EN

ordinary differential equation; nonlinear equation; Cauchy problem; initial-value problem; fixed point; nonexpansive mapping; modular function space; Orlicz space; Musielak-Orlicz space; convex modular

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 13--33
• Opis fizyczny: Bibliogr. 68 poz.

Twórcy

autor

Kozlowski W. M.

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

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