On the existence of periodic solutions for semilinear wave equation on a ball in n with the space dimension n odd

1995 ◽  
Vol 24 (2) ◽  
pp. 241-250 ◽  
Author(s):  
A.K. Ben-Naoum ◽  
J. Berkovits
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Space Dimension ◽  
Semilinear Wave Equation ◽  
Existence Of 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 Infinitely many periodic solutions for a semilinear wave equation with x-dependent coefficients

2020 ◽  
Vol 26 ◽  
pp. 7
Author(s):  
Hui Wei ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Spectral Properties ◽  
Seismic Waves ◽  
Forced Vibrations ◽  
One Dimensional ◽  
Semilinear Wave Equation ◽  
Spatial Interval ◽  
Rational Multiple ◽  
Infinitely Many Periodic Solutions

This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with x-dependent coefficients under various homogeneous boundary conditions. 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 an approximation argument, we prove that there exist infinitely many periodic solutions whenever the period is a rational multiple of the length of the spatial interval. The proof is essentially based on the spectral properties of the wave operator with x-dependent coefficients.

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.

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