Minimal solutions of multivalued differential equations
Consider \(u'\in F(t,u)\), \(u(0)=x_ 0\) with F: [0,a]\(\times {\mathbb{R}}^ n\to 2^{{\mathbb{R}}^ n}\setminus \emptyset\). Let K be an arbitrary cone in \({\mathbb{R}}^ n\) with nonempty interior and assume that there is f(t,x) such that \(f(t,x)\in (t,x)\subset f(t,x)+K\), where f is quasimonotone in x. Among other conditions, F is assumed to be almost lsc. The author is able to prove that there is an increasing sequence of continuous functions converging pointwise to f, and then to prove that the problem has a minimal solution. The merit of the paper lies in the arbitrariness of the cone K.
scientific article; zbMATH DE number 4212490