Nonuniqueness and fractional index convolution complementarity problems

Abstract

Uniqueness of solutions of fractional index convolution complementarity problems (CCPs) has been shown for index $1+\alpha$ with $-1<\alpha\leq0$ under mild assumptions, but not for $0<\alpha<1$. Here a family of counterexamples is given showing that uniqueness generally fails for $0<\alpha<1$. These results show that uniqueness is expected to fail for convolution complementarity problems of the type that arise in connection with solutions of impact problems for Kelvin-Voigt viscoelastic rods.

Keywords

• Convolution complementarity problem
• mechanical impact
• viscoelasticity
• uniqueness