Nonlinear multivalued differential equations with slow and fast
subsystems are considered. Under transitivity conditions on the
fast subsystem, the slow subsystem can be approximated by an
averaged multivalued differential equation. The approximation in
the Hausdorff sense is of order <mml:math alttext="$O(\epsilon^{1/3})$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>&#1013;</mml:mi><mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math> as <mml:math alttext="$\epsilon\rightarrow 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#1013;</mml:mi><mml:mo>&#8594;</mml:mo><mml:mn>0</mml:mn></mml:math>.

International Journal of Mathematics and Mathematical Sciences

Averaging of multivalued differential equations

Abstract

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