Comparison principle based on Minkowski mixed volumes for a family of differential equations
The paper studies a family of differential equations of the form \[ D_HX=F(t,X,\alpha ),\quad X(t_0)=X_0\in K_c({\mathbb R}^n), \] where \(D_H\) is the generalized (Hukuhara) derivative, \(K_c({\mathbb R}^n)\) denotes the space of nonempty compact convex subsets of \({\mathbb R}^n\), \(\alpha \) is the imprecision parameter varying in a compact set \({\mathcal J}\subset {\mathbb R}^d\) and \(F(.,.,.):{\mathbb R}_+\times K_c({\mathbb R}^n)\times {\mathcal J}\to K_c({\mathbb R}^n)\) is continuous. Under certain hypotheses two comparison principles concerning Minkowski mixed volumes are obtained for the problem considered.
scientific article; zbMATH DE number 6856618
scientific article