We study a particular class of nonconvex-valued differential inclusions. We prove the existence of a continuously differentiable solution under a continuity condition on the associated multiple-valued function in the sense of Almgren.
Goblet, J. (2008). A Peano Type Theorem for a Class of Nonconvex-Valued Differential Inclusions. Set-Valued Analysis, 16(7-8), 913-921. https://doi.org/10.1007/s11228-008-0084-x (Original work published 2008)