Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space
Texas State University-San Marcos, Department of Mathematics
We prove the existence of solutions to the differential inclusion ẍ(t) ∈ F(x(t), ẋ(t)) + ƒ(t, x(t), ẋ(t)), x(0) = x0, ẋ(0) = y0, where ƒ is a Carathéodory function and F with nonconvex values in a Hilbert space such that F(x, y) ⊂ γ(∂g(y)), with g a regular locally Lipschitz function and γ a linear operator.
Nonconvex differential inclusions, Uniformly regular functions
Haddad, T., & Yarou, M. (2006). Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space. <i>Electronic Journal of Differential Equations, 2006</i>(33), pp. 1-8.