Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping <MATH>d/dt-f</MATH> in the Spaces <MATH>L_p({\Bbb R},{\Bbb R})</MATH>, <MATH>1\le p\le\infty</MATH>.

We obtain necessary and sufficient conditions for the Lipschitzian invertibility of the differential mapping <MATH>d/dt- \nomathbreak f</MATH>, where <MATH>f\:{\Bbb R}\to{\Bbb R}</MATH> is a continuous mapping, in the spaces <MATH>L_p({\Bbb R},{\Bbb R})</MATH>, <MATH>1\le p\le \nomathbreak \infty</MATH>. [ABSTRACT FROM AUTHOR]