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Article Contents

# On solution manifolds of differential systems with discrete state-dependent delays

For Jibin Li, on the occasion of his 80th birthday

• For differential equations with state-dependent delays the associated initial value problem is well-posed, with differentiable solution operators, on submanifolds of the space $C^1_n=C^1([-r,0],\mathbb{R}^n)$, under mild smoothness assumptions. We study these solution manifolds and find that for a large class of equations their solution manifolds are nearly as simple as a graph over the subspace $X_0\subset C^1_n$ defined by $\phi'(0)=0$. The result supplements recent work on finite atlases of solution manifolds and is related to the open problem whether in some cases the constructed atlases are minimal.

Mathematics Subject Classification: Primary: 34K05, 34K43; Secondary: 58B99.

 Citation:

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