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June 2004 Application of local linking to asymptotically linear wave equations with resonance II
Mieko Tanaka
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SUT J. Math. 40(2): 157-179 (June 2004). DOI: 10.55937/sut/1108749134


Existence of a time-periodic solution to a non-linear wave equation with resonance is established by a variational method. We consider the 2π-periodic weak solution to a wave equation u(x,t)=h(x,t,u(x,t)) of space dimension 1, where h(x,t,ξ) is asymptotically linear in ξ both as ξ0 or ξ, with the co-efficient as ξ belonging to σ(). It was proved that there are some cases, where the difference of h(t,x,ξ) from its linear approximation is not bounded, that guarantee the existence of a non-trivial weak solution. In this paper, we show that the restriction in our previous result imposed on these co-efficients can be further relaxed.


The author would like to thank very much Professor Shizuo Miyajima for helpful comments and encouragement.


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Mieko Tanaka. "Application of local linking to asymptotically linear wave equations with resonance II." SUT J. Math. 40 (2) 157 - 179, June 2004.


Received: 2 November 2004; Published: June 2004
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1108749134

Primary: 35L05 , 35L35 , 47J30 , 58E05

Keywords: (WPS)* condition , asymptotically linear wave equation , existence of a critical point , Local Linking , variational method

Rights: Copyright © 2004 Tokyo University of Science

Vol.40 • No. 2 • June 2004
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