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Zbl 0908.34024
Zhang, Meirong
Periodic solutions of damped differential systems with repulsive singular forces. (English)
[J] Proc. Am. Math. Soc. 127, No.2, 401-407 (1999). ISSN 0002-9939; ISSN 1088-6826/e

Summary: The author considers the periodic boundary value problem for the singular differential system $u''+(\nabla F(u))'+\nabla G(u) = h(t)$, with $F\in C^{2}(\bbfR ^{N}, \bbfR)$, $G\in C^{1}(\bbfR ^{N} \backslash \{0\}, \bbfR)$, and $h\in L^{1}([0,T], \bbfR ^{N})$. 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.

MSC 2000:: *34C15 Nonlinear oscillations of solutions of ODE
34C25 Periodic solutions of ODE

Keywords: singular force; strong force condition; damped system; coincidence degree

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