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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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.

Article information

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

Dates
First available in Project Euclid: 12 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1368397765

Mathematical Reviews number (MathSciNet)
MR1347988

Zentralblatt MATH identifier
0824.34040

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

Citation

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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