Estimates of the area of solutions of the pseudolinear differential equations with Hukuhara derivative in the space $\text{conv} (R^2)$

Abstract

We obtain estimates for the areas of the solutions of differential equations with Hukuhara derivative of a special form in the space $\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v} (R^2)$. The main methods used for the investigation are the method of comparison, the methods of the Minkowski – Aleksandrov geometry of convex bodies, and the Chaplygin –Wa˙zewski method of approximate integration of differential equations. The obtained results enable us to reduce the estimates of the area of solutions to the investigation of differential equations of the first order.