Filippov Lemma for certain second order differential inclusions
The paper is concerned with the following Cauchy problem for a second-order differential inclusion \[ x''\in A^2x+F(t,x),\quad x(0)=0,\quad x'(0)=0, \] where \(A\) is a non-degenerated \(n\times n\) real matrix and \(F:[0,1]\times {\mathbb R}\to {\mathcal P}({\mathbb R})\) is a set-valued map with closed values and Lipschitz in the second variable. An existence result for this problem is derived, starting from a given quasi solution. As usual for a Filippov-type existence theorem, the result provides an estimate between the quasi solution and the obtained solution.
scientific article; zbMATH DE number 6137127
scientific article