Multiple periodic solutions of a superlinear forced wave equation

1992 ◽  
Vol 162 (1) ◽  
pp. 43-76 ◽  
Author(s):  
Kazunaga Tanaka
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Forced Wave ◽  
Multiple Periodic Solutions

Existence of Multiple Periodic Solutions for a Semilinear Wave Equation in an n-Dimensional Ball

2019 ◽  
Vol 19 (3) ◽  
pp. 529-544
Author(s):  
Hui Wei ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Space Dimension ◽  
Semilinear Wave Equation ◽  
Point Reduction ◽  
Working Space ◽  
Linearized Problem ◽  
Multiple Periodic Solutions ◽  
Arbitrary Space ◽  
Dimensional Ball

Abstract This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an n-dimensional ball. By combining the variational methods and saddle point reduction technique, we obtain the existence of at least three periodic solutions for arbitrary space dimension n. The structure of the spectrum of the linearized problem plays an essential role in the proof, and the construction of a suitable working space is devised to overcome the restriction of space dimension.

scholarly journals Existence of multiple periodic solutions to a semilinear wave equation with x-dependent coefficients

2019 ◽  
Vol 150 (5) ◽  
pp. 2586-2606
Author(s):  
Hui Wei ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Seismic Waves ◽  
One Dimensional ◽  
Semilinear Wave Equation ◽  
Point Reduction ◽  
Spatial Interval ◽  
Multiple Periodic Solutions ◽  
Rational Multiple ◽  
Asymptotic Character

AbstractThis paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with x-dependent coefficients. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By combining variational methods with saddle point reduction technique, we obtain the existence of at least three periodic solutions whenever the period is a rational multiple of the length of the spatial interval. Our method is based on a delicate analysis for the asymptotic character of the spectrum of the wave operator with x-dependent coefficients, and the spectral properties play an essential role in the proof.

scholarly journals Multiple Periodic Solutions to a Suspension Bridge Wave Equation with Damping

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Shanshan Wang ◽  
Yukun An
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Degree Theory ◽  
Suspension Bridge ◽  
Damped Wave Equation ◽  
Multiple Periodic Solutions

This paper is concerned with the existence of multiple periodic solutions for a suspension bridge wave equation with damping. By using Leray-Schauder degree theory, the authors prove that the damped wave equation has multiple periodic solutions.

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