Abstract
We give necessary and sufficient conditions for the existence and uniqueness of bounded or almost-periodic solutions of the first-order differential system: $u' + \nabla \Phi (u) = e(t)$, when $\nabla \Phi$ denotes the gradient of a convex function on $\mathbb R^N$. We also study the relations of continuity between the forcing term $e$ and the solution $u$. Then we give similar results for the second-order differential system: $u'' = \nabla \Phi (u) + e(t)$.
Citation
Philippe Cieutat. "Necessary and sufficient conditions for existence and uniqueness of bounded or almost-periodic solutions for differential systems with convex potential." Differential Integral Equations 18 (4) 361 - 378, 2005. https://doi.org/10.57262/die/1356060192
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