Geodesic
Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping $d/dt-f$ in the Spaces $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 891-903.

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We obtain necessary and sufficient conditions for the Lipschitzian invertibility of the differential mapping $d/dt-f$, where $f\colon{\mathbb R}\to{\mathbb R}$ is a continuous mapping, in the spaces $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$. 
@article{MZM_2003_73_6_a10,
     author = {V. E. Slyusarchuk},
     title = {Necessary and {Sufficient} {Conditions} for the {Lipschitzian} {Invertibility} of the {Nonlinear} {Differential} {Mapping} $d/dt-f$ in the {Spaces} $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {891--903},
     publisher = {mathdoc},
     volume = {73},
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V. E. Slyusarchuk. Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping $d/dt-f$ in the Spaces $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 891-903. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a10/

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