Differential and Integral Equations

Multiple solutions for an asymptotically linear wave equation

Marek Izydorek

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Abstract

We will be concerned with the multiplicity results for periodic solutions of the wave equation $(*)$ $u_{tt}-u_{xx}= f(x,t,u)$ satisfying some standard boundary and periodicity conditions. Our aim is to show that under some reasonable conditions on $f$ the above problem possesses at least three solutions in the non--equivariant case and to estimate the number of periodic solutions of $(*)$ when an action of $Z_2$ is involved.

Article information

Source
Differential Integral Equations Volume 13, Number 1-3 (2000), 289-310.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356124301

Mathematical Reviews number (MathSciNet)
MR1811960

Zentralblatt MATH identifier
1038.35038

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35A15: Variational methods 35B10: Periodic solutions 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Izydorek, Marek. Multiple solutions for an asymptotically linear wave equation. Differential Integral Equations 13 (2000), no. 1-3, 289--310. https://projecteuclid.org/euclid.die/1356124301.


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