## Differential and Integral Equations

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

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

Vesa Mustonen and Stanislav PohoŽaev

#### 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