On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces

• Autorzy: W.M. Kozlowski
• 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: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: 53
• Numer: 2

Daty

wydano

2013

online

2014-12-15

Twórcy

autor

W.M. Kozlowski

Identyfikatory

DOI

10.14708/cm.v53i2.779