scholarly journals Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension

2013 ◽  
Vol 66 (10) ◽  
pp. 1541-1581 ◽  
Author(s):  
Raphaël Côte ◽  
Hatem Zaag
Keyword(s):  
Wave Equation ◽  
Space Dimension ◽  
Blowup Solution ◽  
Semilinear Wave Equation ◽  
One Space Dimension

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.

Sign in / Sign up

Export Citation Format

Share Document