Existence of solutions for nonconvex third order differential inclusions
Britney Hopkins · Electronic journal of qualitative theory of differential equations · 2005
This paper proves the existence of solutions for a third order initial value nonconvex differential inclusion. We start with an upper semicontinuous compact valued multifunction $F$ which is contained in a lower semicontinuous convex function $\partial V$ and show that, $$x^{(3)}(t) \in F(x(t),x'(t),x''(t)),\quad x(0)=x_{0}, \quad x'(0)=y_{0}, \quad x''(0)=z_{0}.$$