A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

doi:10.1007/s10473-021-0111-7

Abstract

Abstract: This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemi-variational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions. Finally, an example is presented to illustrate our main results.

Key words: fractional differential variational inequality, fractional nonlinear delay evolution equation, hemi-variational inequality, condensing map, KKM theorem, fixed point theorem

CLC Number:

34A08

Yunhua WENG, Xuesong LI, Nanjing HUANG. A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2021, 41(1): 187-206.

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