Differential and Integral Equations

Subharmonic and multiple subharmonic solutions for second order differential systems

Norimichi Hirano and Naoki Shioji

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We show existence and multiple existence results of subharmonic solutions for the system of second order differential equation $\ddot{u}(t)+ G'(u(t))=f(t)$ for $t\in \mathbb R$, where $N \in \mathbb N$, $f \in C(\mathbb R, \mathbb R^N)$ is a $T$-periodic function, $G\in C^{2}(\mathbb R^{N},\mathbb R)$ is a nonconvex functional.

Article information

Differential Integral Equations, Volume 16, Number 1 (2003), 95-110.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C25: Periodic solutions
Secondary: 47J30: Variational methods [See also 58Exx] 47N20: Applications to differential and integral equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Hirano, Norimichi; Shioji, Naoki. Subharmonic and multiple subharmonic solutions for second order differential systems. Differential Integral Equations 16 (2003), no. 1, 95--110. https://projecteuclid.org/euclid.die/1356060698

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