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2005 Necessary and sufficient conditions for existence and uniqueness of bounded or almost-periodic solutions for differential systems with convex potential
Philippe Cieutat
Differential Integral Equations 18(4): 361-378 (2005).

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: $u'' = \nabla \Phi (u) + e(t)$.

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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.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.34112
MathSciNet: MR2122704

Subjects:
Primary: 34C11
Secondary: 34C12 , 34C27

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 4 • 2005
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