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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Periodic solutions
of damped differential systems
with repulsive singular forces

Author: Meirong Zhang
Journal: Proc. Amer. Math. Soc. 127 (1999), 401-407
MSC (1991): Primary 34C15, 34C25
MathSciNet review: 1637460
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Abstract: We consider the periodic boundary value problem for the singular differential system: $u''+(\nabla F(u))'+\nabla G(u) = h(t),$ where $F\in C^{2}(\mathbb R ^{N}, \mathbb R )$, $G\in C^{1}(\mathbb R ^{N} \backslash \{0\}, \mathbb R )$, and $h\in L^{1}([0,T], \mathbb R ^{N})$. The singular potential $G(u)$ is of repulsive type in the sense that $G(u) \to +\infty $ as $u\to 0$. Under Habets-Sanchez's strong force condition on $G(u)$ at the origin, the existence results, obtained by coincidence degree in this paper, have no restriction on the damping forces $(\nabla F(u))'$. Meanwhile, some quadratic growth of the restoring potentials $G(u)$ at infinity is allowed.

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Additional Information

Meirong Zhang
Affiliation: Department of Applied Mathematics, Tsinghua University, Beijing 100084, People’s Republic of China

Keywords: Singular force, strong force condition, damped system, coincidence degree
Received by editor(s): September 23, 1996
Additional Notes: The author is supported by the National Natural Science Foundation of China and the Tsinghua University Education Foundation
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society