Differential and Integral Equations

On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain

Vesa Mustonen and Stanislav PohoŽaev

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Abstract

We consider nonlinear periodic radial wave equations of the form $$ u_{tt}-u_{rr}-\frac{N-1}r u_r+g(t,r,u)=0,\qquad t\in\mathbb{R},\quad 0<r<R. $$ The main purpose of the paper is to characterize the nonlinearities $g$ such that the equation has no nontrivial periodic solutions in $\mathbb{R}^N$ within a given natural class of functions $u$. The proofs are based on a new integral identity which we introduce for the solutions of the wave equation.

Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 133-145.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414139

Mathematical Reviews number (MathSciNet)
MR1608004

Zentralblatt MATH identifier
1004.35091

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 34B15: Nonlinear boundary value problems 35B10: Periodic solutions

Citation

Mustonen, Vesa; PohoŽaev, Stanislav. On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain. Differential Integral Equations 11 (1998), no. 1, 133--145. https://projecteuclid.org/euclid.die/1367414139


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