A non-convex setup for multivalued differential equations driven by oblique subgradients
The paper studies differential inclusions of the form \[ g(t,x(t))\in x'(t)+H(t,x(t))\partial ^{-}\varphi (x(t)), \quad t\in [0,T],\quad x(0)=x_0,\eqno (1) \] where \(H(.,.): [0,T]\times {\mathbb R}^d\to {\mathbb R}^{d\times d}\) is a matrix application such that \(x\to H(.,x)\) is Lipschitz, \(\varphi (.): {\mathbb R}^d\to (-\infty ,+\infty ]\) is a proper lower semicontinuous semiconvex function and \(x_0\in {\mathbb R}^d\). Under certain technical assumptions existence and uniqueness results for the problem considered are provided. Afterwards the global existence result obtain for problem (1) is applied in order to obtain the existence of a solution for a non-convex Skorokhod problem with generalized reflection.
scientific article; zbMATH DE number 6351524
scientific article