On the superposition operator in the space of functions of bounded variation, revisited. (English) Zbl 1202.45005
Summary: We provide sufficient conditions under which a nonautonomous superposition operator maps the space of functions of bounded variation in the sense of Jordan or Young into itself. We apply these results to examine the existence and uniqueness of solutions to Hammerstein and Volterra-Hammerstein integral equations in those spaces.
MSC:
| 45G10 | Other nonlinear integral equations |
| 47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
Keywords:
Banach contraction principle; Hammerstein integral equation; Volterra-Hammerstein integral equation; variation in the sense of Jordan; \(\varphi \)-variation; nonautonomous superposition operatorReferences:
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