Existence of solutions for nonconvex third order differential inclusions

B. Hopkins, University of Arkansas at Little Rock, Little Rock, USA

E. J. Qualitative Theory of Diff. Equ., No. 22. (2005), pp. 1-11.

Abstract: 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 \emph{F} which is contained in a lower semicontinuous convex function $\partial V$ and show that,

$x^{(3)}(t) \in F(x(t),x'(t),x''(t)),$ $ \: x(0)=x_{0}, \: x'(0)=y_{0}, \: x''(0)=z_{0}$.

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