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Invertibility of the nonlinear operator \(\left( {{\mathcal{L}}x} \right)\left( t \right) = H\left( {x\left( t \right),\;\frac{{dx\left( t \right)}} {{dt}}} \right)\) in the space of functions bounded on the axis

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Nonlinear Oscillations

We obtain conditions for the invertibility of the nonlinear differential operator

$\left( {{\mathcal{L}}x} \right)\left( t \right) = H\left( {x\left( t \right),\;\frac{{dx\left( t \right)}} {{dt}}} \right)$

in the space of functions bounded on the axis.

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Authors and Affiliations

  1. National University of Water Management and Nature Resources Application, Rivne, Ukraine

    V. Yu. Slyusarchuk

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  1. V. Yu. Slyusarchuk
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Correspondence to V. Yu. Slyusarchuk.

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Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 421–436, July–September, 2008.

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Slyusarchuk, V.Y. Invertibility of the nonlinear operator \(\left( {{\mathcal{L}}x} \right)\left( t \right) = H\left( {x\left( t \right),\;\frac{{dx\left( t \right)}} {{dt}}} \right)\) in the space of functions bounded on the axis. Nonlinear Oscill 11, 442–460 (2008). https://doi.org/10.1007/s11072-009-0042-z

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