Differential inclusion for the evolution p(x)-laplacianwith memory

This work was initiated when the authors were supported by the research grants CSF-CAPES-PVE-Process 88881.030388/2013-01 and the program “Science Without Borders”, CSF-CAPES-PVE-Process 88887.059583/2014-00, Brazil. The first author was supported by the Russian Federation government, Grant no. 14.W03.31.0002, Russia; and by the Portuguese Foundation for Science and Technology, Portugal, under the project UID/MAT/04561/2019. The second author acknowledges the support of the Research Grant MTM2017-87162-P, Spain. The third author was partially supported by the Brazilian research agency FAPEMIG process PPM 00329-16. The third and fourth authors was partially supported by the Brazilian research agency FAPEMIG process CEX-APQ-00814-16.