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1995 $T$-periodic solutions for a second order system with singular nonlinearity
Raúl F. Manásevich, Manuel A. del Pino
Differential Integral Equations 8(7): 1873-1883 (1995).

Abstract

We consider a system of the form $$ \begin{align} & u''+au'=H_v(u,v)-h(t) \\ & v''+ bv'=H_u(u,v) - k(t), \end{align} $$ where $h,k $ are locally integrable and $T$-periodic, and $H$ is a $C^1$ function defined on $(0,\infty)\times (0,\infty)$, for which a good model is given by $$ H(u,v) = -( {1\over u^\alpha } + {1\over v^\beta } ),\quad \alpha ,\beta > 0 . $$ We state conditions under which existence of positive, $T$-periodic solutions for this system is ensured. We also study the problems of uniqueness and existence of multiple solutions in some special cases.

Citation

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Raúl F. Manásevich. Manuel A. del Pino. "$T$-periodic solutions for a second order system with singular nonlinearity." Differential Integral Equations 8 (7) 1873 - 1883, 1995.

Information

Published: 1995
First available in Project Euclid: 12 May 2013

zbMATH: 0824.34040
MathSciNet: MR1347988

Subjects:
Primary: 34C25
Secondary: 34B15, 47H15, 47N20

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 7 • 1995
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