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1998 On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain
Vesa Mustonen, Stanislav PohoŽaev
Differential Integral Equations 11(1): 133-145 (1998).

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.

Citation

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Vesa Mustonen. Stanislav PohoŽaev. "On the nonexistence of periodic radial solutions for semilinear wave equations in unbounded domain." Differential Integral Equations 11 (1) 133 - 145, 1998.

Information

Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1004.35091
MathSciNet: MR1608004

Subjects:
Primary: 35L70
Secondary: 34B15, 35B10

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 1 • 1998
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