Differential and Integral Equations

$T$-periodic solutions for a second order system with singular nonlinearity

Raúl F. Manásevich and Manuel A. del Pino

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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.

Article information

Differential Integral Equations, Volume 8, Number 7 (1995), 1873-1883.

First available in Project Euclid: 12 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C25: Periodic solutions
Secondary: 34B15: Nonlinear boundary value problems 47H15 47N20: Applications to differential and integral equations


del Pino, Manuel A.; Manásevich, Raúl F. $T$-periodic solutions for a second order system with singular nonlinearity. Differential Integral Equations 8 (1995), no. 7, 1873--1883. https://projecteuclid.org/euclid.die/1368397765

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