This publication covers two theorems on the existence of solutions of differential inclusions with the current velocity in which the right side and turn to the current velocity , and the right side for the inclusion of the quadratic derivative average are multivalued. Two cases are considered : • when , among other conditions , the right- turn for the quadratic derivative average is an upper semicontinuous • when , among other conditions , the right- turn for the quadratic derivative average is lower semicontinuous.
Mean derivatives, stochastic differential inclusions with current velocity
1. Gliklikh Yu.E. Global and Stochastic Analysis with Applications to Mathematical Physics / Yu.E. Gliklikh.- London: Springer-Verlag, 2011.- 460 p.
2. Azarina S.V. Diferential inclusions with mean derivatives /S.V. Azarina and Yu.E.Gliklikh// Dynamic Systems and Applications.- 2007.- Vol. 16, No. 1.- P. 49-71 3. Gliklikh Yu.E., Makarova A.V. Belgorod State University Scientific bulletin Mathematics.Physics.-2012.No.17(136).ISSU 28.-P. 5-16