Averaging of perturbed one sided Lipschitz differential inclusions (Q1770177)

The authors study an averaging method for upper semicontinuous differential inclusions in Banach spaces of the form \[ \dot x(t)\in F(t,x)+G\left(\frac{t}{\varepsilon},x\right), \,\, x(0)=x_0, \quad t\in [0,a], \,\, x\in E, \] where \(F(\cdot,\cdot), G(\cdot,\cdot)\) have nonempty convex and compact values, \(F(t,\cdot)\) is one-sided Lipschitz and maps bounded sets into bounded sets and \(E\) a Banach space with uniformly convex dual. The averaging of functional-differential inclusions is studied, too.