Electron. J. Diff. Equ., Vol. 2014 (2014), No. 226, pp. 1-9.

Nonuniqueness and fractional index convolution complementarity problems

David E. Stewart

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.

Submitted June 4, 2014. Published October 22, 2014.
Math Subject Classifications: 90C33, 74M20, 34A08.
Key Words: Convolution complementarity problem; mechanical impact; viscoelasticity; uniqueness.

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David E. Stewart
Department of Mathematics, University of Iowa
Iowa City, IA 52242, USA
email: david-e-stewart@uiowa.edu

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