Periodic solutions for second order differential inclusions with nonconvex and unbounded multifunction
The authors consider boundary value problems \(x''(t) \in F\big(t,x(t),x'(t)\big)\) a.e. on \([0,b],\) \(x(0)=x(b)\) and \(x'(0)=x'(b),\) where \(F\) is an unbounded and nonconvex set-valued function. They transform it into a periodic problem with convex and bounded right-hand side via Filippov regularization of a directionally continuous selector and show that solutions to the latter problem also solve the original problem. The paper generalizes results of \textit{S. Hu} and \textit{N. S. Papageorgiou} [Proc. Am. Math. Soc. 123, No.~10, 3043-3050 (1995; Zbl 0851.34014)] where the authors studied first-order periodic differential inclusions with a nonconvex multifunction by a similar approach.
scientific article; zbMATH DE number 1404412