Geodesic
On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces
Commentationes Mathematicae, Tome 53 (2013) no. 2, p. 113−133.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/cm.v53i2.779
Mots-clés : ordinary differential equation, nonlinear equation, Cauchy problem, initial value problem, fixed point, nonexpansive mapping, modular function space, Orlicz space, Musielak-Orlicz space, convex modular 
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W.M. Kozlowski. On Nonlinear Differential Equations in Generalized Musielak-Orlicz Spaces. Commentationes Mathematicae, Tome 53 (2013) no. 2, p.  113−133. doi : 10.14708/cm.v53i2.779. http://geodesic.mathdoc.fr/articles/10.14708/cm.v53i2.779/

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